Question

A mass is sliding from rest down a smooth inclined plane with an inclination angle, calculate the velocity after it travels a distance along the incline

Answer 1

Answer:

the answer is

$v = \sqrt{2gl \sin(theta) }$

Explanation:

Since the mass is sliding down a smooth inclined plane there will be no frictional force providing resistance to the mass and it will slide down by gravitational pull.

g acts downwards always,

See the figure where I have drawn the components of acceleration due to gravity (g) along the plane.

let length of incline plane be l

therefore, along the incline velocity will be after it has travelled a distance l,

${v}^{2} = {u}^{2} + 2al \\ {v }^{2} =0 + 2 \times g \sin(theta) \times l \\ {v}^{2} = 2gl \sin(theta) \\ v = \sqrt{2gl \sin(theta)}$