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 \[BP=a\] |
\[\therefore \] \[x=OM=a\sin \theta =asin\,(2t)\] |
Hence M executes SHM within the given time period and its acceleration is opposite to 'x' that means towards left |
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