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

\ u = $\sqrt{5gr}$ = g$\sqrt{5}$ ….. (1)

\ velocity is vertical at point B

\ Acceleration is at point B is

a = $\sqrt{a_{t}^{2} + a_{c}^{2}}$ a = $\sqrt{g^{2} + \left( \frac{v^{2}}{r} \right)^{2}}$… (2)

\ v² = u² – 2gr = 3gr

\ a = $\sqrt{g^{2} + (3g)^{2}}$ = $g\sqrt{10}$