Hc Verma I for Class 12 Science Physics Chapter 4 - The Forces

Answer:

The Earth is pulling the body with an action force mg. This force is exerted by the body on the table. In turn, the table exerts equal and opposite reaction force ($-mg$) on the body in the upwards direction which balances the weight of the body. 

Answer:

The given situation involves two action-reaction pairs of forces. They are:

(a) The action force (F = mg) with which the boy pushes the chair in the downward direction and the reaction force (F' = $-$mg) with which the chair exerts on the boy in the upward direction.
(b) The action force (F = (M + m)g) with which the boy and the chair push the ground in the downward direction and the reaction force (F' = (M + m)g) with which the ground exerts on the boy and the chair in the upward direction.

Answer:

The police may beat the lawyer's client until he issues a statement of confession. This force does not have any physical significance in physics. Hence, it is not a force of physics.

Answer:

When we hold a pen and write on our notebook, we are exerting electromagnetic force on the pen. The pen is also exerting the same force on the notebook. We are also exerting gravitational force on the notebook.

Answer:

Yes, it is true that the reaction of a gravitational force is always gravitational and that of an electromagnetic force is always electromagnetic and so on. For example, if the Earth exerts a gravitational action force on the Moon, then the Moon will also exert the same gravitational reaction force on it. Similarly, when a comb, just after being used, is brought near a piece of paper, it exerts an electromagnetic action force on the paper and the paper will also exert an electromagnetic reaction force on it.

Answer:

First let us calculate the coulomb force between 2 protons for distance = 8 fm
$$\begin{gathered} F\mathit{ }\mathit{=}\frac{\mathit{K}\mathit{ }{\mathit{q}}^{\mathit{2}}}{{\mathit{r}}^{\mathit{2}}} \\ =\frac{9\times {10}^9\times (1.6\times {10}^{-19}{)}^2}{(8\times {10}^{-15}{)}^2} \\ =3.6 \mathrm{N} \end{gathered}$$
$$\begin{gathered} F_{\mathrm{N}} = 0.05 \mathrm{N} \\ \frac{F_{\mathrm{N}}}{F_{\mathrm{C}}} = \frac{0.05}{3.6} = 0.0138 \mathrm{N} \end{gathered}$$
For x= 4 fm
$$\begin{gathered} F_{\mathrm{C}} = \frac{9\times {10}^9\times (1.6\times {10}^{-19}{)}^2}{(4\times {10}^{-15}{)}^2} \\ =\frac{23.04\times {10}^{-29}}{(4\times {10}^{-15}{)}^2} \\ =14.4 \mathrm{N} \\ {F}_{\mathrm{N}}= 1\mathrm{N} \\ \frac{F_{\mathrm{N}}}{F_{\mathrm{C}}} = \frac{1}{14.4} = 0.0694 \mathrm{N} \\ \mathrm{For} x=2 \mathrm{fm} \\ {F}_{\mathrm{C}}=\frac{9\times {10}^9\times (1.6\times {10}^{-19}{)}^2}{(2\times {10}^{-15}{)}^2} \\ =57.6 \mathrm{N} \\ {F}_{\mathrm{N}}= 10 \mathrm{N} \\ \frac{F_{\mathrm{N}}}{F_{\mathrm{C}}} = \frac{10}{57.6} =0.173 \\ \mathrm{For} x=1 \mathrm{fm} \\ {F}_{\mathrm{C}} = \frac{9\times {10}^9\times (1.6\times {10}^{-19}{)}^2}{(1\times {10}^{-15}{)}^2} \\ =230.4 \mathrm{N} \\ {F}_{\mathrm{N}} = 1000 \mathrm{N} \\ \frac{F_{\mathrm{N}}}{F_{\mathrm{C}}} = \frac{1000}{230.4} = 4.34 \end{gathered}$$

Answer:

Forces acting on block B:

• A pair of electromagnetic forces between the blocks A and B.
• A pair of electromagnetic forces between the blocks B and the Earth.
• A pair of gravitational forces between the blocks B and the Earth.
• A pair of gravitational forces between the blocks A and B.
• A pair of action-reaction forces between the man and block A.
• Weight of the man, block A and block B as action forces on the ground in the downward direction.
• Reaction of the ground on the man, block A and block B in the upward direction to balance their weights.

Answer:

Forces acting on the pulley A:

1. A tension exerts electromagnetic force between the string and pulley A.
2. A pair of gravitational force between the Earth and pulley.

1. A tension exerts electromagnetic force between the string and the boy.
2. A pair of gravitational force between the Earth and the boy.

1. A tension exerts electromagnetic force between the string and block C.
2. A pair gravitational force between block C and the Earth.

Answer:

List of forces:

(a) A pair of gravitational force between the wagon and the Earth.
(b) A frictional force exerted by the road on the wagon.
(c) A tension exerts electromagnetic force between the wagon and string.
(d) A pair of gravitational force between the man and the Earth.
(e) A frictional force exerted by the road on the man.
(f) A tension exerts electromagnetic force between the man and string.

Here, (a), (c), (d) and (f) are pairs of forces associated with Newton's third law of motion.

Answer:

Answer:

(b) Electromagnetic

When Neils Bohr shook hand with Werner Heisenberg, electromagnetic force is exerted on each other. This is because when their hands made contact with each other, the atoms at the two surfaces come close to each other. The charged constituents of the atoms in the hands exert forces on each other and, as a result, a measurable force is produced.

Answer:

(d) E>G>N

Between two electrons at a given separation, the strongest acting force is the electromagnetic force. The gravitational force is the weakest force between any two particles. There is no nuclear force acting between them, because it exists only in the nucleus (between proton-proton or neutron-neutron or both).

Answer:

(d) irrespective of the signs of the charges.

The sum of all electromagnetic forces between different particles of a system of charged particles is zero irrespective of the sign of the charges, because electromagnetic force is a vector quantity that depends upon the direction. So, we consider the directions while adding vector quantities.

Answer:

(c) 60 N

According to Newton's third law, which states that an action-reaction pair of forces are equal in magnitude, the man who weighs 40 kg will push the other man with the same force of 60 N.

Answer:

(a) gravitational
(c) nuclear

A neutron exerts both the gravitational and nuclear forces on a proton.
The gravitational force can be seen between a neutron and a proton. However, its strength is negligible. The nuclear force is exerted only if the interacting particles are neutrons or protons or both. A neutron cannot exert electromagnetic force, because it is a neutral particle.

Answer:

(a) gravitational
(b) electromagnetic
(c) nuclear

A proton exerts gravitational, electromagnetic and nuclear forces on a proton.
The gravitational force can easily be seen everywhere; it the weakest among all the forces. It is negligible in elementary particles like protons.
The electromagnetic force can be seen between charged particles. Since proton is a charged particle, it can exert this force on other protons.
The nuclear force is present only if the interacting particles are protons or neutrons or both. So, this force can exist between two protons.

Answer:

(b) The electromagnetic force between two protons is always greater than the gravitational force between them.
(c) The gravitational force between two protons may be greater than the nuclear force between them.
(d) Electromagnetic force between two protons may be greater than the nuclear force acting between them.

The electromagnetic force between two protons is always greater than the gravitational force between them, because gravitational force is the weakest force in nature.
We know that nuclear force is the strongest force in nature when the distance between two particles is less than ${10}^{-14} \mathrm{m}$. However, the gravitational as well as electromagnetic forces between two protons may be greater than the nuclear force acting between them when the distance between them is more than ${10}^{-14} \mathrm{m}$.

Answer:

(a) there would be no force of friction
(b) there would be no tension in the string
(c) it would not be possible to sit on a chair

For the existence of friction between two bodies and tension in a string, electromagnetic force is needed. Electromagnetic force exists only between charged particles. For sitting on a chair, we need fractional force. A neutral particle can exert gravitational force on other neutral particles. So, even if all the matters were made up of electrically neutral particles, the earth will still move around the sun.

Answer:

(a) motion of a cricket ball
(b) motion of a dust particle

Classical physics adequately describes the motion of a ball and the motion of dust particles. It also describes Newton's law of motion, Newton's law of gravitation, Laws of thermodynamics, Maxwell's electromagnetism and Lorentz force. Classical physics easily describes the system of heavenly bodies like the Sun, the Earth and the Moon. However, it is inadequate for describing systems of particles which have sizes much smaller than ${10}^{-6} \mathrm{m}$ (e.g., atom, nuclei and other elementary particles).

Answer:

(a) the right end is displaced towards right and the left end towards left
(d) the right end is displaced towards left and the left end towards right.

When the right end is displaced towards the right and the left end towards the left, then this is the case of tension (expansion) and the spring will have maximum displacement.

When the right end is displaced towards the left and the left end towards the right, then this is the case of compression and ,again, the spring will have maximum displacement.

Answer:

(a) act on two different objects
(b) have equal magnitude
(c) have opposite directions
(d) have resultant zero.

The two forces $\overrightarrow{F} \mathrm{and} -\overrightarrow{F}$ connected by Newton's third law are known as action-reaction pair.
For example, when a man jumps out from a ferry, he applied some force on the ferry. So, the action force in this case is the force applied by the man and the reaction is the force exerted by the ferry on the man. Both the forces act upon different objects (the man and the ferry) but have equal magnitudes and opposite directions. As a result, their resultant is zero.

Answer:

Mass of the particle, m = 1 gm$=\frac{1}{1000} \mathrm{kg}$
Let the distance between the two particles be r.
Gravitational force between the particle, F = 6.67 × 10⁻¹⁷ N
Also, $\mathrm{F}=\frac{G{m}_1{m}_2}{r^2}$
Substituting the respective values in the above formula, we get:
$$\begin{gathered} 6.67\times {10}^{-17}=\frac{6.67\times {10}^{-11}\times \left(1/1000\right)\times \left(1/1000\right)}{r^2} \\ \Rightarrow r^2=\frac{6.67\times {10}^{-6}\times {10}^{-11}}{6.67\times {10}^{-17}} \\ =\frac{{10}^{-17}}{{10}^{-17}}=1 \\ \Rightarrow r=\sqrt{1}=1 \mathrm{m} \end{gathered}$$
∴ The separation between the particles is 1 m.

Answer:

Consider that a man is standing on the surface of the Earth.
Force acting on the man = mg
Here, m = mass of the man and g = acceleration due to gravity on the surface of earth (=10 m/s²)

Assume that the mass of the man is equal to 65 kg.
Then F = W = mg = 65 × 10 = 650 N = force acting on the man
∴ By Newton's third law (action-reaction are always equal), the man is also attracting the earth with a force of 650 N in the opposite direction.

Answer:

Given: $q_1=q_2=1 \mathrm{C}$

By Coulomb's law, the force of attraction between the two charges is given by
$$\begin{gathered} F=\frac{1}{4\mathrm{\pi }{\in }_0}\frac{q_1{q}_2}{r^2} \\ =\frac{9\times {10}^9\times 1\times 1}{r^2} \end{gathered}$$
However, the force of attraction is equal to the weight (F = mg).
$$\begin{gathered} \therefore mg=\frac{9\times {10}^9}{r^2} \\ \Rightarrow r^2=\frac{9\times {10}^9}{m\times 10}=\frac{9\times {10}^8}{m} (\mathrm{Taking} g=10 \mathrm{m}/{\mathrm{s}}^2) \\ \Rightarrow r^2=\frac{9\times {10}^8}{m} \\ \Rightarrow r=\frac{3\times {10}^4}{\sqrt{m}} \end{gathered}$$

Assuming that m = 81 kg, we have:
$$\begin{gathered} r=\frac{3\times {10}^4}{\sqrt{81}} \\ =\frac{3}{9}\times {10}^4 \mathrm{m} \\ =3333.3 \mathrm{m} \end{gathered}$$

∴ The distance r is 3333.3 m.

Answer:

Mass = 50 kg
Separation between the masses, r = 20 cm = 0.2 m
Let the change on each sphere be q.
Now, gravitational force, $F_{\mathrm{G}}=G\frac{m_1{m}_2}{r^2}$
                                          $$\begin{gathered} =\frac{67\times {10}^{-11}\times {\left(50\right)}^2}{{\left(0.2\right)}^2} \\ =\frac{67\times {10}^{-11}\times 2500}{0.04} \end{gathered}$$

$$\begin{gathered} \mathrm{Coulomb} \mathrm{force}, F_{\mathrm{c}}=\frac{1}{4\mathrm{\pi }{\in }_0}\frac{q_1{q}_2}{r^2} \\ =9\times {10}^9\frac{q^2}{0.04} \end{gathered}$$
Since F_G = F_c, we have:

$$\begin{gathered} \frac{6.7\times {10}^{-11}\times 2500}{0.04}=\frac{9\times {10}^9\times q^2}{0.04} \\ \Rightarrow q^2=\frac{6.7\times {10}^{-11}\times 2500}{9\times {10}^9} \\ =\frac{9\times {10}^9}{0.04}=1809\times {10}^{-18} \\ \therefore q=\sqrt{18.09\times {10}^{-18}} \\ =4.3\times {10}^{-9} \mathrm{C} \end{gathered}$$

Thus, the charge of the spherical body is $4.3\times {10}^{-9} \mathrm{C}$.

Answer:

Given: The limb of the tree exerts a normal force of 48 N and a frictional force of 20 N.



So, resultant magnitude of the force if given by
$$\begin{gathered} R=\sqrt{\left({48}^2+{20}^2\right)} \\ =\sqrt{2304+400} \\ =\sqrt{2704}=52 \mathrm{N} \end{gathered}$$

∴ The magnitude of the total force exerted by the limb on the monkey is 52 N.

Answer:

Force exerted by the body builder against the bullworker = 150 N
Compression in the bullworker, x = 20 cm = 0.2 m

∴ Total force exerted, f = kx = 150
Here, k is the spring constant of the spring in the bullworker.

$\therefore k=\frac{150}{0.2}=\frac{1500}{2}=750 \mathrm{N}/\mathrm{m}$

Hence, the spring constant of the spring in the bullworker is 750 N/m.

Answer:

Let h be the height, M be the Earth's mass, R be the Earth's radius and m be the satellite's mass
.
Force on the satellite due to the earth when it is at the Earth's surface, $F_1=\frac{\mathrm{GM}m}{{\mathrm{R}}^2}$

Force on the satellite due to the earth when it is at height h above the Earth's surface, $F_2=\frac{\mathrm{GM}m}{{\left(\mathrm{R}\mathit{+}h\right)}^2}$

According to question, we have:
$$\begin{gathered} \frac{F_1}{F_2}=\frac{{\left(R+h\right)}^2}{R^2} \\ \Rightarrow 2=\frac{{\left(R+h\right)}^2}{R^2} \\ \mathrm{Taking} \mathrm{squareroot} \mathrm{on} \mathrm{both} \mathrm{sides}, \mathrm{we} \mathrm{get}: \\ \sqrt{2}=1+\frac{h}{R} \\ \Rightarrow h=\left(\sqrt{2}-1\right)R \\ =0.414\times 6400=2649.6 \mathrm{km}\approx 2650 \mathrm{km} \end{gathered}$$

Answer:

Two charged particles placed at a separation of 20 cm exert 20 N of Coulomb force on each other.
So, $F_1=\frac{1}{4\mathrm{\pi }{\in }_0}·\frac{q^2}{r_1^2}$
Also, $F_2=\frac{1}{4\mathrm{\pi }{\in }_0}·\frac{q^2}{r_2^2}$
According to the question, we have:
$$\begin{gathered} \frac{F_2}{F_1}=\frac{r_1^2}{r_2^2} \\ =\frac{20\times 20}{25\times 25}=\frac{16}{25} \\ \therefore F_2=\frac{16}{25}\times F_1 \end{gathered}$$
$$\begin{gathered} \Rightarrow F_2=\frac{16}{25}\times 20 \\ \Rightarrow F_2=12.8 \mathrm{N} \approx 13.0 \mathrm{N} \end{gathered}$$

Therefore, the two charged particles will exert a force of 13.0 N on each other, if the separation is increased to 25 cm.

Answer:

The force between the Earth and the Moon is given by $F=\frac{\mathrm{G}Mm}{r^2}$.
Here, M is the mass of the earth; m is the mass of the moon and r is the distance between Earth and Moon.

On substituting the values, we get:
$F=\frac{6.67\times {10}^{-11}\times 7.36\times {10}^{22}\times 6\times {10}^{24}}{3.8\times 3.8\times {10}^{16}}$

$$\begin{gathered} =\frac{6.67\times 7.36\times {10}^{35}}{(3.8{)}^2\times {10}^{16}} \\ =20.3\times {10}^{19}=2.03\times {10}^{20} \\ \approx 2.0\times {10}^{20} \mathrm{N} \end{gathered}$$

∴ The weight of the moon is $2.0\times {10}^{20} \mathrm{N}$.

Answer:

Charge of the proton, q = $1.6\times {10}^{-19} \mathrm{C}$
Mass of the proton = $1.67\times {10}^{-27} \mathrm{kg}$
Let the distance between two protons be r.
Coulomb force (electric force) between the protons is given by
$$\begin{gathered} f_e=\frac{1}{4\mathrm{\pi }{\in }_0}\times \frac{q^2}{r^2} \\ =\frac{9\times {10}^9\times (1.6{)}^2\times {10}^{-38}}{r^2} \end{gathered}$$
Gravitational force between the protons is given by
$$\begin{gathered} f_g=\frac{\mathrm{G}{m}^2}{r^2} \\ =\frac{6.67\times {10}^{-11}\times (1.67\times {10}^{-27}{)}^2}{r^2} \end{gathered}$$

On dividing $f_e \mathrm{by} f_g$, we get:
$$\begin{gathered} \frac{f_e}{f_g}=\frac{1}{4\mathrm{\pi }{\in }_0}\times \frac{q^2}{r^2}\times \frac{r^2}{\mathrm{G}{m}^2} \\ =\frac{9\times {10}^9\times 1.6\times 1.6\times {10}^{-38}}{6.67\times {10}^{-11}\times 1.67\times 1.67\times {10}^{-54}} \\ =\frac{9\times (1.6{)}^2\times {10}^{-29}}{6.67\times (1.67{)}^2\times {10}^{-65}} \\ =1.24\times {10}^{36} \end{gathered}$$

Answer:

Average separation between the proton and the electron of a Hydrogen atom in ground state, r = 5.3 × 10⁻¹¹ m

(a) Coulomb force when the proton and the electron in a hydrogen atom in ground state
$$\begin{gathered} F=9\times {10}^9\times \frac{q_1{q}_2}{r_2} \\ =\frac{9\times {10}^9\times {\left(1.6\times {10}^{-19}\right)}^2}{{\left(5.3\times {10}^{-11}\right)}^2}=8.2\times {10}^{-8} \mathrm{N} \end{gathered}$$

(b) Coulomb force when the average distance between the proton and the electron becomes 4 times that of its ground state
$$\begin{gathered} \mathrm{Coulomb} \mathrm{force}, F=\frac{1}{4\mathrm{\pi }{\in }_0}=\frac{q_1{q}_2}{{\left(4r\right)}^2} \\ =\frac{9\times {10}^9\times {\left(1.6\times {10}^{-19}\right)}^2}{16\times {\left(5.3\right)}^2\times {10}^{-22}} \\ =\frac{9\times {\left(1.6\right)}^2}{10\times {\left(5.3\right)}^2}\times {10}^{-7} \\ =0.0512\times {10}^{-7} \\ =5.1\times {10}^{-9} \mathrm{N} \end{gathered}$$

Answer:

The geostationary orbit of the Earth is at a distance of about 36000 km.
We know that the value acceleration due to gravity above the surface of the Earth is given by $g\text{'}=\frac{\mathrm{G}m}{{\left(R+h\right)}^2}$.
At h = 36000 km, we have:
$g\text{'}=\frac{\mathrm{G}m}{{\left(36000+6400\right)}^2}$
At the surface, we have:
$$\begin{gathered} g=\frac{\mathrm{G}m}{{\left(6400\right)}^2} \\ \therefore \frac{g\text{'}}{g}=\frac{6400\times 6400}{42400\times 42400} \\ =\frac{256}{106\times 106}=0.0228 \\ \Rightarrow g\text{'}=0.0227\times 9.8=0.223 \left[\mathrm{Taking} g=9.8 \mathrm{m}/{\mathrm{s}}^2 \mathrm{at} \mathrm{the} \mathrm{surface} \mathrm{of} \mathrm{the} \mathrm{earth}\right] \end{gathered}$$

For a 120 kg equipment placed in a geostationary satellite, its weight will be
mg' = 120 × 0.233
$\Rightarrow$26.76 ≈ 27 N