EASY

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Any net force causing uniform circular motion is called a tangential force.

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Important Questions on Circular Motion

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A conical pendulum of length

l

makes an angle

θ = 45 °

with respect to

Z -

axis and moves in a circle in the

X Y

plane. The radius of the circle is

0.4 m

and its center is vertically below

O

. The speed of the pendulum, in its circular path, will be -

(T a k e g = 10 m s^{- 2})

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A particle of mass

m

is suspended from a ceiling through a string of length

L

. The particle moves in a horizontal circle of radius

r

such that

r = \frac{L}{\sqrt{2}}

. The speed of particle will be :

EASY

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A car is moving in a circular horizontal track of radius

10 m

with a constant speed of

10 m s^{- 1}

. A bob is suspended from the roof of the car by a light wire of length

1.0 m

. The angle made by the wire with the vertical is (in radian)

EASY

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A car is moving in a circular path of radius

450 m

with a speed of

30 m s^{- 1}

. If the speed of the car is increased at a rate of

2 m s^{- 2}

, the resultant acceleration will be,

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A spherical bob hangs from a light inextensible string and moves in a horizontal circle with string making angle

θ

with the vertical. The length

l

of the string is then very slowly increased so that the motion is circular at all times to a good approximation. If

h

is the height from center of the circle to the pivot and

r

is the radius of the circle then

h \propto r^{a}

. The value of

a

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A disc of radius

0.4 m

and mass

1 kg

rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration is

10 rad / s^{2} .

The tangential force applied to the rim of the disc is

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

70 kg

man stands in contact against the inner wall of a hollow cylindrical drum of radius

3 m

rotating about its vertical axis with

200 rev / \min

. The coefficient of friction between the wall and his clothing is

0.15

. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A disc of radius

R

has a light pole fixed perpendicular to the disc at the circumference which in turn has a pendulum of length R attached to its other end as shown in figure. The disc is rotated with a constant angular velocity

ω

. The string is making an angle

45 °

with the rod. Then the angular velocity

ω

of disc is

Question Image

HARD

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A particle of mass

m

is rotating in a horizontal circle of radius

R

and is attached to a hanging mass

M

, as shown in the figure. The speed of rotation required by the mass

m

to keep

M

steady is

HARD

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A heavy small-sized sphere is suspended by a string of length

L

. The sphere is rotated uniformly in a horizontal circle with the string making an angle

θ

with the vertical. The time period of this conical pendulum is,

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A particle rests on the top of a hemisphere of radius R. Find the smallest horizontal velocity that must be imparted to the particle, if it is to leave the hemisphere without sliding down it.

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

Two particles of equal mass are revolving in circular paths of radii r₁ and r₂ respectively with the same angular velocity. The ratio of their centripetal forces will be

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A block is rotating in a circular track and angular speed of the block is given by,

ω = a t^{2}

. Where,

ω

is in

r a d s^{- 1}

and

t

is in seconds,

a

is a constant and equal to

2 r a d s^{- 3}

. Mass of the block is

1 k g

and radius of circular track is

1 m

. Net force acting on the block at

t = 2 s

is -

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

$A B C D$ is a smooth horizontal fixed plane on which mass $m_{1} = 0.1 kg$ is moving in a circular path of radius $1 m$ . It is connected by an ideal string which is passing through a smooth hole and connects mass $m_{2} = \frac{1}{\sqrt{2}} kg$ at the other end as shown. $m_{2}$ also moves in a horizontal circle of same radius of $1 m$ with a speed of $\sqrt{10} m s^{- 1}$ . If $g = 10 m s^{- 2}$ , then the speed of $m_{1}$ is–

Question Image

EASY

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A stone of mass $0.3 kg$ , attached to a $1.5 m$ long string, is whirled around in a horizontal circle on a frictionless table, at a speed of $6 m s^{- 1}$ . The tension in the string is

EASY

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A ball of mass

m = 0.5 kg

is attached to the end of a string having length

L = 0.5 m

. The ball is rotated on a horizontal circular path about the vertical axis. The maximum tension that the string can bear is

324 N

. The maximum possible value of the angular velocity of ball (in

rad s^{- 1}

) is

HARD

Science>Physics>Circular Motion>Tangential and Radial Acceleration

$A B C D$ is a smooth horizontal fixed plane on which mass $m_{1} = 0.1 k g$ is moving in a circular path of radius $1 m$ . It is connected by an ideal string which is passing through a smooth hole and connects mass $m_{2} = \frac{1}{\sqrt{2}} k g$ at the other end as shown. $m_{2}$ also moves in a horizontal circle of same radius of $1 m$ with a speed of $\sqrt{10} m / s$ . If $g = 10 m / s^{2}$ , then the speed of $m_{1}$ is-

Question Image

HARD

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A heavy small-sized sphere is suspended by a string of length

l

. The sphere is rotated uniformly in a horizontal circle with the string making an angle

θ

with the vertical. The time period of this conical pendulum is

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A string of length

L

is fixed at one end and carries a mass

M

at the other end. The string makes

2 / π

revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is-

Question Image

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A stone of mass

0.25 kg

tied to the end of a string is whirled round in a circle of radius

1.5 m

with a speed of

40 rev / \min

in a horizontal plane. What is the tension in the string? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of

200 N

Any net force causing uniform circular motion is called a tangential force.

Important Questions on Circular Motion

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