A rod PQ of length l is moving with ends remaining in contact with frictionless wall and floor. If at the instant, shown the velocity of end Q is 2 m/s towards negative direction of x. The speed of end P will be

$\sqrt{3} {ms}^{- 1}$

$\frac{2}{\sqrt{3}} {ms}^{- 1}$

$\sqrt{2} {ms}^{- 1}$

$\frac{\sqrt{5}}{2} {ms}^{- 1}$

Solution

$\frac{2}{\sqrt{3}} {ms}^{- 1}$

From the diagram in question

x = l cosθ

y = l sinθ

∴ $v_{x} = \frac{dx}{dt}$ = -l sinθ $\frac{dθ}{dt}$ ..... $(\frac{d}{dt} cosθ = - sinθ)$

v_y = $\frac{dy}{dt}$ = l cosθ $\frac{dθ}{dt}$

∴ $\frac{v_{y}}{v_{x}} = - \cot θ$ ..... $(\frac{\cos θ}{\sin θ} = \cot θ)$

v_y = - v_x cot θ

Since v_x = -2 m/s

v_y = -2 cot 60^o ....( Given:- θ = 60^o )

= $- 2 \times \frac{1}{\sqrt{3}}$

v_y = $- \frac{2}{\sqrt{3}}$ ms^-1

The negative sign indicates the motion towards negative direction of Y.

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Motion In Straight Line

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Motion In Straight Line

A rod PQ of length l is moving with ends remaining in contact with frictionless wall and floor. If at the instant, shown the velocity of end Q is 2 m/s towards negative direction of x. The speed of end P will be 3 ms-1 23 ms-1 2 ms-1 52 ms-1

Some More Questions From Motion in Straight Line Chapter

What is motion?

Is absolute rest or absolute motion possible?

What is the most essential thing to study the motion of a body?

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

A particle is moving along curved line in space. Is the motion one dimensional?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation