A particle slides on surface of a fixed smooth sphere starting from top most point. The angle rotated by the radius through the particle, when it leaves contact with the sphere, is

$θ = \cos^{- 1} \frac{1}{3}$

$θ = \cos^{- 1} (\frac{2}{3})$

$θ = \tan^{- 1} (\frac{1}{3})$

$θ = \sin^{- 1} \frac{4}{3}$

Solution

$θ = \cos^{- 1} (\frac{2}{3})$

See the diagram

Let the velocity be v when the body leaves the surface. From free body diagram,

$\frac{{mv}^{2}}{R} = mg cosθ$

⇒ v² = R g cosθ

Again from work-energy principle

change in KE = work done

⇒ $\frac{1}{2} {mv}^{2} - 0 = mg (R - R cosθ)$

v² = 2gR ( 1 - cosθ)

From Eqs. (i) and (ii)

Rg cosθ = 2gR ( 1 - cosθ )

⇒ 3 gR cosθ = 2gR

⇒ $θ = \cos^{- 1} (\frac{2}{3})$

Some More Questions From Laws of Motion Chapter

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Laws Of Motion

Some More Questions From Laws of Motion Chapter

Define inertia.

When the branches of an apple tree are shaken, the apples fall down. Why?

A person jumping out from a moving car or bus falls forward. Why?

Due to what type of inertia, the spark leaves the grind stone tangentially while sharpening the knife?

Which law of motion is also called law of inertia?

What is measure of inertia of body?

Which law of motion defines the force?

What happens to a stone tied to the end of string and whirled in a circle if the string suddenly breaks?

Which law of motion gives the quantitative knowledge of force?

Which law of motion is the real law of motion?

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Laws Of Motion

A particle slides on surface of a fixed smooth sphere starting from top most point. The angle rotated by the radius through the particle, when it leaves contact with the sphere, is θ =cos-1 13 θ = cos-1 23 θ = tan-1 13 θ = sin-1 43

Some More Questions From Laws of Motion Chapter

Define inertia.

When the branches of an apple tree are shaken, the apples fall down. Why?

A person jumping out from a moving car or bus falls forward. Why?

Due to what type of inertia, the spark leaves the grind stone tangentially while sharpening the knife?

Which law of motion is also called law of inertia?

What is measure of inertia of body?

Which law of motion defines the force?

What happens to a stone tied to the end of string and whirled in a circle if the string suddenly breaks?

Which law of motion gives the quantitative knowledge of force?

Which law of motion is the real law of motion?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation