question_answer

A rod of length \[\ell \] is in motion such that its ends A and B are moving along x-axis and y-axis respectively. It is given that \[\frac{d\theta }{dt}=2\] rad/s always. P is a fixed point on the rod. Let \[M\] be the projection of \[P\] on x-axis. For the time interval in which \[\theta \] changes from 0 to \[\frac{\pi }{2}\] choose the correct statement:

A) The acceleration of \[M\] is always directed towards right

B) \[M\] executes SHM

C) \[M\] moves with constant speed

D) \[M\] moves with constant acceleration

Correct Answer: B

Solution :

\[\frac{d\theta }{dt}=2\]             \[\therefore \theta =2t\]

Let \[BP=a\,\,\therefore \,\,x=OM=\alpha \,\sin \theta =\alpha \sin \,(2t)\]

Hence M executes SHM within the given time period and its acceleration is opposite to 'x' that means towards left