Question

The motion of particle of mass m is given by x = 0 for t < 0 s , x (t) = A sin4p t for 0 < t < (1/4) s ( A > 0), and x = 0 for t > (1/4) s. Which of the following statement is true?

• A. The force at t = (1/8) s on the particle is $-a6{\pi }^{2}Am$
• B. The particle is acted upon by on impulse of magnitude $4{\pi }^{2}Am$ at t = 0 s and t = ( 1/4) s.
• C. The particle is not acted upon by any force.
• D. The particle is not acted upon by a constant force.
• E. There is no impulse acting on the particle.

Answer 1

Answer: (A), (B), (D)

The correct options are
A The force at t = (1/8) s on the particle is $-a6{\pi }^{2}Am$
B The particle is acted upon by on impulse of magnitude $4{\pi }^{2}Am$ at t = 0 s and t = ( 1/4) s.
D The particle is not acted upon by a constant force.

Correct option are A,B and D

For different time intervals position of the particle is given. Hence, we have to find velocity and acceleration corresponding to the intervals.

The impulse (Change in linear momentum) at t = 0 is same as t = 1/4 s. Hence, option (b) is correct.

We know that, force depends upon acceleration and which is not constant here. Hence, force is also not constant. Hence option (d) is also correct.

Important point: We have to keep in mind that the force is varying for different time intervals. Hence, we should apply differential formulae for each interval separately