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A particle is moving in a circular path of radius $R_{0}$ with a constant speed $v_{0} .$ If the particle's speed is decreased by a factor of $β$ i.e., $v' = \frac{v_{0}}{β}$ and the radius of circular path is doubled, then, the centripetal acceleration decreases by a factor ${mβ}^{n} .$ The value of $mn$ is _____.

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Important Questions on Motion in a Plane

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 49

Two particles

A

and

B

are revolving on two coplanar circles with time periods

4

second and

6

second respectively. Time period of particle

A

with respect to

B

will be

n s .

The value of

n

is _____.

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 50

Speed of a particle moving on a circular path of radius

2 m

is varying with time as

v = (t^{2}) m s^{- 1} .

Net acceleration of the particle at

t = 2

second is

8 \sqrt{n} m s^{- 2} .

The value of

n

is _____.

EASY

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IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 51

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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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 _____.

EASY

JEE Main/Advance

IMPORTANT

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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IMPORTANT

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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IMPORTANT

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})

A particle is moving in a circular path of radius R0 with a constant speed v0. If the particle's speed is decreased by a factor of β i.e., v'=v0β and the radius of circular path is doubled, then, the centripetal acceleration decreases by a factor mβn. The value of mn is _____.

Important Questions on Motion in a Plane

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