Question

A solid sphere rolls down from top of inclined plane, 7m high, without slipping. Its linear speed at the foot of plane is ______. (g = 10 m/s²)

पर्याय

• `sqrt70`

• `sqrt(140/3)`m/s

• `sqrt(280/3)`m/s

• `sqrt100` m/s

Answer 1

A solid sphere rolls down from top of inclined plane, 7m high, without slipping. Its linear speed at the foot of plane is `underline(sqrt100 "m"/"s")`.

Explanation:

Given, height of inclined plane, h = 7 m

g = 10 m/s² 

By conservation of energy,

Potential energy lost by the solid sphere in rolling down the inclined plane = Kinetic energy gained by the sphere.

mgh = `1/2 "mv"^2 + 1/2 "k"omega^2`

= `1/2 "mv"^2 + 1/2 * 2/5 "mR"^2 * ("v"/"R")^2`

`= 1/2 "mv"^2 + 1/5 "mv"^2`

mgh = `7/10 "mv"^2`

`therefore "v"^2 = 10/7`gh

`=> "v" = sqrt(10/7 "gh")`

`= sqrt(10/7 xx 10 xx 7)`

`= sqrt100` m/s