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Column-I shows some bodies (ring, disc, hollow sphere, solid sphere) rolling without slipping on horizontal surface. Two forces $F_{1}$ and $F_{2}$ are acting at different points parallel to surface. Column-II gives direction and magnitude of static friction between bodies and surface. Match column-II with column-I.
Column-I Column-II
A)
P) Direction of friction must be in positive x-axis
B)
Q) Direction of friction must be in negative x-axis
C)
R) Magnitude of friction must be 2N
D)
S) Magnitude of friction must be 4N
T) Direction and magnitude of friction can be found if and only if mass and radius is given

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A-QR, B-QR, C-PS, D-R

A-QR, B-QS, C-QR, D-R

A-PR, B-QS, C-QS, D-Q

A-QR, B-QR, C-QS, D-QR

answer is D.

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Detailed Solution

If $F_{1}$ is absent then in first three cases friction acts to the left. So the direction and magnitude of friction in first three cases is decided by point of application of $F_{2}$ and the moment of inertia of respective bodies.
For friction to be absent for pure rolling.
Point of application of force be x (say) above the centre.
Then

$10-f=Ma fR= \frac{2}{3} {MR}^{2} \frac{a}{R} 10-f= \frac{3}{2} f \frac{5f}{2} =10 \Rightarrow f=4$

$fR-2× \frac{2}{5} R= \frac{2}{5} {MR}^{2} \frac{a}{R} 5-f=Ma f- \frac{4}{5} = \frac{2}{5} Ma 5-f= \frac{5}{2} (f- \frac{4}{5}) 7= \frac{7f}{2} \Rightarrow f=2N$

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