First slide

Rolling motion

Question

A solid sphere of mass 10 kg is placed on a rough surface having coefficient of friction $μ = 0.1$ . A constant force F = 7 N is applied along a line passing through the centre of the sphere as shown in the figure. The value of frictional force on the sphere is

Moderate

A

1 N
B

2 N
C

3 N
D

7 N

Solution

Let f be frictional force towards left for pure rolling.
$a = Rα$
where, $a = \frac{F - f}{m} = \frac{7 - f}{10}$
$α = \frac{τ}{I} = \frac{fR}{I} = \frac{fR}{\frac{2}{5} {mR}^{2}} = \frac{5 f}{2 mR}$
Hence, $\frac{7 - f}{10} = \frac{5 f}{10} \Rightarrow f = 2 N$

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