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A disc of radius $1 m$ is rotating about central axis with angular velocity $2 rad s^{- 1} .$ If a point $P$ lying on its circumference as shown is moving with velocity $4 \hat{j} m s^{- 1},$ then speed of centre of disc is $\sqrt{n} m s^{- 1} .$ The value of $n$ is _____.

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Important Questions on Motion in a Plane

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JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 52

A particle is performing motion whose position vector is given by

\vec{r} = 15 (\cos p t \hat{i} + \sin p t \hat{j}) m,

when

p

is in

rad s^{- 1}

and

t

is in seconds. The magnitude of centripetal acceleration at

t = 3 s,

n p^{2} m s^{- 2} .

The value of

n

is _____.

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 53

A particle is performing circular motion in a circle of radius

R

with variable speed,

v = Kt (K > 0) .

Time when angle between acceleration vector and its velocity vector becomes

\frac{π}{4},

4 \sqrt{\frac{R}{nK}} .

The value of

n

is _____.

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 54

A particle moves along a curve

y = x^{2}

with constant speed of

10 m s^{- 1} .

When the particle is at origin, then the radius of curvature of path is

n m .

The value of

n

is _____.

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 1

A particle moves on the curve

y = \frac{x^{2}}{4},

where

x = \frac{t}{2} .

x

and

y

are measured in metre and

t

in second. At

t = 4 s,

the velocity of particle is

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IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 2

One second after projection, a stone moves at an angle of

45 °

with the horizontal. Two seconds after projection, it moves horizontally. Its angle of projection is (in degrees)

(g = 10 m s^{- 2})

HARD

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IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 3

The horizontal range of a projectile is

R

and the maximum height attained by it is

H .

A strong wind now begins to blow in the direction of horizontal motion of projectile, giving it a constant horizontal acceleration equal to

g .

Under the same conditions of projection, the new range will be
(

g =

acceleration due to gravity)

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IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 4

The speed of a projectile when it is at its maximum height is

\sqrt{\frac{2}{5}}

times its speed at half the maximum height. What is its angle of projection?

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 5

If the horizontal range of projectile be a and the maximum height attained by it is

b,

then velocity of projection is

A disc of radius 1 m is rotating about central axis with angular velocity 2 rad s–1. If a point P lying on its circumference as shown is moving with velocity 4j^ m s–1, then speed of centre of disc is n m s–1. The value of n is _____.

Important Questions on Motion in a Plane

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A disc of radius $1 m$ is rotating about central axis with angular velocity $2 rad s^{- 1} .$ If a point $P$ lying on its circumference as shown is moving with velocity $4 \hat{j} m s^{- 1},$ then speed of centre of disc is $\sqrt{n} m s^{- 1} .$ The value of $n$ is _____.