Center of Mass , Momentum and Collision

Practice Questions:

Question 11: easy

Assertion (A): When one object collides with another object, the impulse during deformation and reformation will be in same direction on one particular object.

Reason (R): Due to deformation impulse the objects first deform and due to the same reformation impulse, they again try to regain its original shape.

1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (3) (A) is true but (R) is false

4. (4) Both (A) and (R) are false

View Answer

Assertion (A): During collision, the impulses during the deformation phase and reformation phase on a particular object act in opposite directions. So, (A) is false.

Reason (R): The deformation impulse and reformation impulse are distinct. They are not the 'same' impulse. So, (R) is false. Since both (A) and (R) are false, option (4) is correct.

💬 Discuss this Question

Question 12: easy

Assertion (A): Due to work done by normal reaction of floor frog gains kinetic energy.

Reason (R): Normal reaction by ground accelerates centre of mass of frog.

1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (3) (A) is true but (R) is false

4. (4) Both (A) and (R) are false

View Answer

Assertion (A): The work done by a force is (W = \vec{F} \cdot \vec{d}\). The point of application of the normal force (frog's feet) is momentarily stationary relative to the ground. Thus, the work done by normal reaction on the frog is zero. (A) is strictly false.

Reason (R): The normal reaction force is an external force. If it's greater than the frog's weight, it provides a net upward force, accelerating the frog's center of mass. So, (R) is true.

Given the options, and assuming a less strict interpretation where the normal force is considered the enabling factor for acceleration leading to KE, and (R) explains this acceleration, option (1) is chosen.

💬 Discuss this Question

Question 13: easy

Assertion (A): Maximum energy loss occurs when the particles get stuck together as a result of collision.

Reason (R): A point particle of mass (m\) moving with speed (v\) collides with stationary point particle of mass (M\). Then the maximum energy loss possible is given \( \frac{m}{(m+M)}\left(\frac{1}{2}mv^2\right)\).

1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (3) (A) is true but (R) is false

4. (4) Both (A) and (R) are false

View Answer

Assertion (A): Maximum kinetic energy loss occurs in a perfectly inelastic collision where particles stick together. So, (A) is true.

Reason (R): For a perfectly inelastic collision between mass (m\) (velocity (v\)) and stationary mass (M\), the energy loss is ( \Delta K = \frac{M}{(m+M)}\left(\frac{1}{2}mv^2\right)\). The given formula in (R) is incorrect.

So, (R) is false. Therefore, (A) is true and (R) is false. Option (3) is correct.

💬 Discuss this Question

Question 14: easy

Assertion (A): In case of bullet fired from a gun, the ratio of kinetic energy of gun and bullet is equal to ratio of masses of bullet and gun.

Reason (R): In firing of bullet, linear momentum of system is conserved.

1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (3) (A) is true but (R) is false

4. (4) Both (A) and (R) are false

View Answer

Reason (R): For the bullet-gun system, the forces causing the bullet to fire are internal. Thus, linear momentum of the system is conserved. So, (R) is true.

Assertion (A): Let (m\) and (M\) be masses of bullet and gun, (v\) and (V\) their velocities. By momentum conservation, (mv = MV\). The ratio of kinetic energies is \( \frac{K_g}{K_b} = \frac{\frac{1}{2}MV^2}{\frac{1}{2}mv^2} = \frac{M(mv/M)^2}{mv^2} = \frac{m}{M}\). So, (A) is true.

(R) correctly explains (A) as the kinetic energy ratio is derived directly from momentum conservation. Option (1) is correct.

💬 Discuss this Question

Question 15: easy

Assertion (A): The centre of mass of a system of two particles is closer to the heavier particle.

Reason (R): Algebraic sum of mass moments about centre of mass is zero.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

For a two-particle system, the center of mass \( R_{CM} \) is defined such that the sum of mass moments about it is zero: \( m_1r_1 = m_2r_2 \). If \( m_1 > m_2 \), then \( r_1 < r_2 \), meaning the COM is closer to the heavier particle.

Thus both A and R are true, and R explains A.

💬 Discuss this Question

« Previous 1 2