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Motion of Center of Mass

Practice Questions:

Question 1: easy

Assertion (A): Two particles undergo rectilinear motion along different straight lines. Then the centre of mass of system of given two particles also always moves along a straight line.

Reason (R): If direction of net momentum of a system of particles (having non-zero net momentum) is fixed, the centre of mass of given system moves along a straight line.

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

Both (A) and (R) are true. The velocity of the center of mass is given by \(V_{CM} = \frac{P_{total}}{M_{total}}\). If particles move rectilinearly, their velocities are constant, making \(P_{total}\) constant in direction. A fixed direction of \(V_{CM}\) means rectilinear motion. Hence, (R) correctly explains (A).

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Question 2: 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.

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