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 ______.

Options

• g `sqrt10`

• g

• g `sqrt2`

• 3g

Answer 1

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 g `bb(sqrt10)`.

Explanation:

u² = 5gR

∴ v² = u² - 2gR

= 5gR - 2gR

= 3gR

Tangential acceleration at B is

a_t = g (downwards)

Centripetal acceleration at B is

a_c = `"v"^2/"R"` = 3g

∴ Total acceleration will be

a = `sqrt("a"_"c"^2+"a"_"t"^2)`

= g `sqrt10`