question_answer

A sphere of mass ?m? is given some angular velocity   about   a horizontal axis through its centre and gently placed on a plank of mass ?m The coefficient of friction between the two is\[\mu \]. The plank rests on a smooth horizontal surface. The initial acceleration of the plank is

A) Zero  

B)        \[(7/5)\mu g\]

C) \[\mu g\] 

D) \[2\mu g\]

Correct Answer: C

Solution :

[c] FBD for sphere and block \[{{a}_{1}}=\frac{{{f}_{r}}}{m}=\frac{\mu mg}{m},\,\,\,{{a}_{2}}=\frac{{{f}_{r}}}{m}=\frac{\mu mg}{m}\] \[\overset{\to }{\mathop{{{a}_{1}}}}\,=\mu g\hat{i},\,\,\,\,\overset{\to }{\mathop{{{a}_{2}}}}\,-\mu g\hat{i}\]