A plank of mass `m_(1)` with a uniform solid sphere of mass `m_(2)` placed on it rests and a force `F` is applied to the plank. The acceleration of the plank provided there is no sliding between the plank and the sphere is `(F/(m_(1)+n/7m_(2)))` then the value of `n` is

Answer

2

Explanation

The situation is as shown in the figure
Here we have,
`F-f=m_(1)a_(p)....(i)`
and `f=m_(2)a_(2).....(ii)`
Futher, `fxxr=Ialpha=2/5 m_(2)r^(2)alpha`
and, `a_(p)=a_(c)+alphar`

Substituting the of `f` from equations `(2)`
equations `(1)`, we get
`F-ma_(2)a_(c)=m_(1)a_(p)`
Now we substituting the value of `a_(p)` from equations (4) in equations (5), hence
`F-m_(2)a_(c)=m_(1)(a_(c)+alphar).....(6)`
From equation (2) and (3) or, `alphar=5/2 a_(c)`
Substituting this value in equation (6), we have
or, `F-m_(2)a_(c)=7/2m_(1)a_(c)` or, `F=(m_(2)+7/2m_(1))a_(c)` or, `a_(c)=F/(m_(2)+7/2m_(1))`
Now, `a_(p)=a_(c)+alphar=7/2a_(c)=F/(m_(1)+2/7m_(2))`