First list includes the name of object kept on a frictionless horizontal surface. Radius of the object is r. A constant horizontal force is applied on the object at a heighth above the centre. Object is found to perform pure rolling Second list includes possible value of h according to nature of object. Match the two lists.

Options

A. `{:(P,Q,R,S),(4,1,2,3):}`
B. `{:(P,Q,R,S),(3,1,2,4):}`
C. `{:(P,Q,R,S),(3,4,2,1):}`
D. `{:(P,Q,R,S),(4,2,1,3):}`

Answer

A

Explanation

Force diagram of the object is shown in figure.

In the horizontal direction we can write the following:
`a=(F)/(m)`
For rotational motion about the centre of object we can write the following:
`Fh=I alpha rArr alpha=(Fh)/(I)`
For pure rolling.
`(a=r alpha rArr (F)/(m)= r(Fh)/(I)) rArr h=(I)/(mr) " "...(i)`
We can use moment of inertia (1) according to nature of object.
Ring : `h=(I)/(mr)=(mr^(2))/(mr)=r`
Hollow sphere `h=(I)/(mr)=((2)/(3) mr^(2))/(mr)=(2)/(3) r`
Disce : `h=(I)/(mr)=((1)/(2) mr^(2))/(mr)=(1)/(2)r`
Solid sphere : `h=(I)/(mr) -((2)/(5) mr^(2))/(mr)=(2)/(5) r`