First list includes the name of object rolling down an inclined plane. Inclined plane makes an angle with the horizontal. Friction is sufficient enough for pure rolling Second list includes linear acceleration of object along the plane. Match the two lists.

Options

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

Answer

C

Explanation

Force acting on the object are as shown in the figure.

For pure rolling we can write angular acceleration `alpha=(a)/(r)`.
Equation for the linear motion along the plane can be written as follows:
`mg sin theta-f = ma " ".....(i)`
Equation for rotational motion about the centre of object can be written as follows:
`fr=I alpha rArr fr=I(a)/(r)`
`rArr =(Ia)/(r^(2)) " ".....(ii)`
Substituting from equation (ii) in equation (i) we get
`a=(mg sin theta)/(m+(I)/(r^(2))) " "...(iii)`
We can use moment of inertia (I) according to nature of object.
Ring: `a=(mg sin theta)/(m+m)=(1)/(2) g sin theta`
Hollow sphere : `a=(mg sin theta)/(m+(2)/(3)m)=(3)/(5) g sin theta`
Disce `: a=(mg sin theta)/(m+(1)/(2))m)=(2)/(g) g sin theta`
Solid sphere `: a=(mg sin theta/(m+(2)/(5) m)=(5)/(7) g sin theta`