Question

A solid sphere of mass M and radius R is placed on a smooth horizontal surface. It is given a horizontal impulse J at a height h above the centre of mass and sphere starts rolling then, the value of h and speed of centre of mass are –

• A. h = $\frac{2}{5}$ R and v = $\frac{J}{M}$
• B. h = $\frac{2}{5}$R and v = $\frac { 2 } { 5 }$ $\frac{J}{M}$
• C. h = $\frac{7}{5}$R and v = $\frac { 7 } { 5 }$ $\frac{J}{M}$
• D. h = $\frac{7}{5}R$and v = $\frac{J}{M}$

Answer 1

Answer: (A)

h = $\frac{2}{5}$ R and v = $\frac{J}{M}$

Answer 2

Let the force producing impulse J is F then

F × h = $\frac{2}{5}$mR² × a

and F = ma (where a = Ra)

\ mah = $\frac{2}{5}$mRa ̃ h = $\frac{2}{5}$R

Also impulse = change in momentum

or J = Mv