Question

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

Options

• `"g"  sqrt10  "m"//"s"^2`

• `3  "g"  "m"//"s"^2`

• `"g"  sqrt2  "m"//"s"^2`

• `"g"  "m"//"s"^2`

Answer 1

A particle is given an initial speed u inside a smooth spherical shell of radius R = 1 m so that it is just able to complete the circle. Acceleration of the particle when it is in vertical circle is `"g"  sqrt10  "m"//"s"^2`.

Explanation:

Vertical velocity at bottom,

`"u"^2 = 5"gR"`

`therefore "v"^2 = "u"^2 - 2"gR"`

` = 5"gR" - 2"gR"`

` = 3"gR"`

Tangential acceleration at bottom is a₁ = g (downwards) Centripetal acceleration at bottom is

`"a"_"c" = "v"^2/"R" = 3"g"`

Total acceleration will be

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

`"g" = sqrt10  "m"//"s"^2`