Question

A particle is given an initial speed u inside a smooth spherical shell of radius R = 1 m that it is just able to complete the circle. Acceleration of the particle when its velocity is vertical is –

• A. g$\sqrt{10}$
• B. g
• C. g $\sqrt{2}$
• D. 3g

Answer 1

Answer: (A)

g$\sqrt{10}$

Answer 2

u² = 5gR

\ v² = u² – 2gR

= 5gR – 2gR = 3gR

Tangential acceleration at B is

a_t = g (downwards)

Centripetal acceleration at B is

a_C = $\frac{v^{2}}{R}$ = 3g

\ Total acceleration will be

a = $\sqrt{a_{C}^{2} + a_{t}^{2}}$ = g $\sqrt{10}$