First slide

Rolling motion

Question

A solid sphere of mass m is lying at rest on a rough horizontal surface. The coefficient of friction between the ground and sphere is $μ$ . The maximum value of F, so that the sphere will not slip, is equal to

Moderate

A

$\frac{7}{5} μmg$
B

$\frac{4}{7} μmg$
C

$\frac{5}{7} μmg$
D

$\frac{7}{2} μmg$

Solution

As sphere is rolling we can apply torque equation about point of contact (about P).
$\begin{array}{l} FR = I_{P} α \\ \Rightarrow FR = (\frac{7}{5} {MR}^{2}) α \\ \Rightarrow Rα = \frac{5 F}{7 M} = a \end{array}$
Equation of translatory motion
$F - f = Ma \Rightarrow f = \frac{2}{7} F$ ………(i)
For no sliding, $f \leq μmg \Rightarrow F = \frac{7}{2} μmg$

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