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Minimum velocity required to complete vertical circle of radius $R$ at lowest point is $\sqrt{5 gR}$ .

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Important Questions on Work, Energy and Power

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Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A ball is released from rest from point $P$ of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point $Q$ is $A$ while angular position of point $Q$ is $α$ with respect to point $P$ . Which of the following graphs represent the correct relation between $A$ and $α$ when ball goes from $Q$ to $R$ ?

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HARD

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A small block slides down from the top of hemisphere of radius $R = 3 m$ as shown in the figure. The height $h$ at which the block will lose contact with the surface of the sphere is $m$ . (Assume there is no friction between the block and the hemisphere)

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MEDIUM

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A stone tide to a string of length

L

is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed

u

. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is

\sqrt{x (u^{2} - g L)}

. The value of

x

EASY

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius

R

so that it can complete the loop?

MEDIUM

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to :

(Take the radius of the drum to be 1.25 m and its axle to be horizontal) :

MEDIUM

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A body initially at rest and sliding along a frictionless track from a height $h$ (as shown in the figure) just completes a vertical circle of diameter $A B = D$ . The height $h$ is equal to,
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EASY

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A stone of mass

m

, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is

HARD

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A small bob tied at one end of a thin string of length

1 m

is describing a vertical circle so that the maximum and minimum tension in the string is in the ratio

5 : 1

. The velocity of the bob at the highest position is ______

m s^{- 1}

. (Take

g = 10 m s^{- 2}

)

MEDIUM

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A mass

m

is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break, when

EASY

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A heavy mass is attached at one end of a thin wire and whirled in a vertical circle. The chances of breaking the wire are maximum when

MEDIUM

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A string of length

1 m

is fixed at its one end and a body is attached to the other end of the string. The body oscillates along an arc of a circle in a vertical plane. If the breaking strength of the string is twice the weight of the body, then the maximum distance covered by the body in one oscillation is

EASY

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A particle is released on a vertical smooth semicircular track from point

X

so that,

O X

makes angle

θ

from the vertical (see figure). The normal reaction of the track on the particle vanishes at the point

Y

where

O Y

makes an angle

ϕ

with the horizontal. Then

MEDIUM

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

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EASY

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

For a particle moving in vertical circle, the total energy at different positions along the path.

EASY

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A bob of mass

M

is suspended by a massless string of length

L

. The horizontal velocity

v

at position

A

is just sufficient to make it reach point

B

. The angle

θ

at which the speed of the bob is half of that at

A

satisfies

HARD

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A bead of mass

m

can slide without friction along a vertical ring of radius

R

. One end of a spring of force constant

k = \frac{3 m g}{R}

is connected to the bead and the other end is fixed at the centre of the ring. Initially, the bead is at the point

A

and due to a small push it starts sliding down the ring. If the bead momentarily loses contact with the ring at the instant when the spring makes an angle of

60 °

with the vertical, then the natural length of the spring is

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HARD

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A stone tied to a string of length

L

is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed

u

. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is,

HARD

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A section of fixed quarter circular track of radius R in vertical plane is shown below. A block is released from point A and leaves the path at B. The radius of curvature of its trajectory when it just leaves the path B will be :

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EASY

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A smooth sphere of radius R and M is placed on the smooth horizontal floor. Another particle of mass m is placed on the sphere and a horizontal force F is applied on the sphere as shown. If the particle does not slip on the sphere, then the value of force F is
Question Image

EASY

Physics>Mechanics>Work, Energy and Power>Motion in a Vertical Circle

A pendulum has angular amplitude

θ

. Tension in the string at extreme position is T₁ and at bottom is T₂.

If T₂ = 2T₁ , then

θ

is equal to

Minimum velocity required to complete vertical circle of radius R at lowest point is 5gR.

Important Questions on Work, Energy and Power

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Minimum velocity required to complete vertical circle of radius $R$ at lowest point is $\sqrt{5 gR}$ .