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What is the maximum magnitude of change in velocity of a motorcycle moving with a uniform speed $v_{0}$ in a circular path of length $I = \frac{π}{3} R$ and radius $R ?$ Treat motorcycle as a particle.

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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 44

A particle is performing circular motion in a circle of radius

R

in such a way that at every moment magnitude of its tangential and radial acceleration is equal. If initial velocity of particle is

v_{0}

then time period of

1^{st}

revolution is

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 45

A boy standing in a trolley car projects a stone perpendicular to the trolley car with a speed

v .

If the trolley car moves with a constant velocity

u,

the time of flight of the stone is

\frac{nv}{g} .

The value of

n

is _____.

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 46

Rain is falling vertically with a speed of

4 m s^{- 1} .

After some time, wind starts blowing with a speed of

3 m s^{- 1}

in the north to south direction. In order to protect himself from rain, a man standing on the ground should hold his umbrella at an angle

θ

given by

θ = \tan^{- 1} (\frac{m}{n})

with vertical towards north. If

m, n

are coprime then value of

m n

is _____.

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Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 47

A gun fitted on the top of a moving car is aimed in the backward direction at an angle

60 °

with the horizontal. If the muzzle velocity of the bullet fired from the gun is

8 m s^{- 1},

then the speed of the car for which the bullet comes out vertically is

n m s^{- 1} .

The value of

n

is _____.

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IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 3 - Motion in a Plane>Assignment>Q 48

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 _____.

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

JEE Main/Advance

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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What is the maximum magnitude of change in velocity of a motorcycle moving with a uniform speed v0 in a circular path of length I=π3R and radius R? Treat motorcycle as a particle.

Important Questions on Motion in a Plane

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What is the maximum magnitude of change in velocity of a motorcycle moving with a uniform speed $v_{0}$ in a circular path of length $I = \frac{π}{3} R$ and radius $R ?$ Treat motorcycle as a particle.