Question

A solid sphere of mass M and radius R is lying on a rough horizontal plane. A constant force F = 4 Mg acts vertically at point P such that OP makes 600 with horizontal. Find the minimum value of coefficient of friction m so that sphere starts pure rolling –

• A. $\frac { 3 } { 7 }$
• B. $\frac { 4 } { 7 }$
• C. $\frac { 2 } { 7 }$
• D. $\frac { 2 } { 5 }$

Answer 1

Answer: (C)

$\frac { 2 } { 7 }$

Answer 2

Let a is acceleration and a is angular acceleration of sphere then

a = Ra

4Mg R cos 60⁰ – fR = $\frac { 2 } { 5 }$ MR²a

̃ 2Mg – f = $\frac { 2 } { 5 }$ Ma and f = Ma

̃ a = $\frac { 10 } { 7 } \mathrm {~g}$ ̃ f = $\frac { 10 } { 7 } \mathrm { Mg }$

f £ µ(Mg + 4Mg)

̃ $\frac { 10 } { 7 }$ Mg £ µ5mg ̃ µ_min = $\frac { 2 } { 7 }$