Question

A particle is projected with a speed $v_{\circ }=\sqrt{gR}$. The coefficient of friction between the particle and the hemi-sphere plane is $\mu$$=0.5$. Then, the acceleration of the particle is

• A. $g$
• B. $\frac{\sqrt{5}g}{2}$
• C. $\sqrt{2}g$
• D. None of these

Answer 1

The correct option is B $\frac{\sqrt{5}g}{2}$

When the particle comes in contact with the hemisphere surface, it will slide and friction will be of kinetic in nature. This kinetic friction will provide tangential acceleration to the particle. Tangential acceleration of the particle,
$a_t=\frac{\mu mg}{m}=\mu g=\frac{g}{2}$

Normal(centripetal) acceleration of the particle,
$a_n=\frac{{v_{\circ }}^2}{R}=\frac{gR}{R}=g$
Net acceleration of the particle,
$a_{net}=\sqrt{{a_n}^2+{a_t}^2}=\sqrt{g^2+\frac{g^2}{4}}=\frac{\sqrt{5}g}{2}$