Question

A particle of mass 'm' kept at origin is subjected to a force $\overrightarrow{F}$ = (pt – qx)$\widehat{i}$where 't' : time elapsed and x : x-coordinate of position of particle. Particle starts its motion at t = 0 with zero initial velocity. If p and q are positive constants, then –

• A. Acceleration of the particle will continuously keep on increasing with time
• B. Particle will execute S.H.M.
• C. Force on particle will have no upper limit
• D. The acceleration of particle varies sinusoidally with time

Answer 1

Answer: (D)

The acceleration of particle varies sinusoidally with time

Answer 2

F = pt – qx

⇒ a = $\frac{p}{m}t - \frac{q}{m}x$

⇒ $\frac{d^{2}a}{dt^{2}} = - \left( \frac{q}{m} \right)a$