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As per given figure to complete the circular loop what should be the radius if initial height is $5 m$

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A mass of $0.5 kg$ moving with a speed of $1.5 m s^{- 1}$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k = 50 N m^{- 1}$ . The maximum compression of the spring would be

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MEDIUM

Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

A particle

(m = 1 k g)

slides down a frictionless track

(A O C)

starting from rest at a point

A

(height

2 m

). After reaching

C,

the particle continues to move freely in air as a projectile. When it reaches its highest point

P

(height

1 m

), the kinetic energy of the particle (in

J

) is: (Figure drawn is schematic and not to scale; take

g = 10 m s^{- 2}

) ______________.
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EASY

Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to:

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Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

A uniform chain of mass

M

and length

L

is lying on a smooth horizontal table, with half of its length hanging down. The work done in pulling the entire chain up the table is

MEDIUM

Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies

3.8 \times 10^{7}

J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take

g = 9.8 m s^{- 2}

MEDIUM

Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

A body is moving unidirectionally under the influence of a source of constant power. The square of its displacement in time

t

is proportional to

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Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

A mass

m

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

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Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

A body is released from a height of

30 m

vertically downwards. The speed of the body at which potential energy is twice that of kinetic energy is (Acceleration due to gravity

= 10 m s^{- 2}

)

EASY

Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

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?

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Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

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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Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

A mass of

2 kg

, initially at a height of

1.2 m

above an uncompressed spring with spring constant

2 \times 10^{4} N m^{- 1},

is released from rest to fall on the spring. Taking the acceleration due to gravity as

10 m s^{- 2}

and neglecting the air resistance, the compression of the spring in

mm

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Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

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

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Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

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

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Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

An asteroid of mass

m

is approaching earth, initially at a distance

10 R_{e}

with speed

v_{i} .

It hits Earth with a speed

v_{f},

(R_{e}

and

M_{e}

are radius and mass of earth

)

, then

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Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

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

MEDIUM

Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

A body of mass

2 kg

is thrown vertically up so that its kinetic energy is

490 J

(g = 9.8 m / s^{2})

. The height at which the kinetic energy becomes half the original value is

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Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

A large block of wood of mass $M = 5.99 kg$ is hanging from two long massless cords. A bullet of mass $m = 10 g$ is fired into the block and gets embedded in it. The (block $+$ bullet) then swing upwards, their center of mass rising a vertical distance $h = 9.8 cm$ before the (block $+$ bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before the collision is: (Take $g = 9.8 {m s}^{- 2}$ )

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Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

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) :

EASY

Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

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

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Physics>Mechanics>Work, Energy and Power>Conservative Force and Potential Energy

Consider two masses with

m_{1} > m_{2}

connected by a light inextensible string that passes over a pulley of radius

R

and moment of inertia

I

about its axis of rotation. The string does not slip on the pulley and the pulley turns without friction. The two masses are released from rest separated by a vertical distance

2 h .

When the two masses pass each other, the speed of the masses is proportional to

As per given figure to complete the circular loop what should be the radius if initial height is 5 m

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As per given figure to complete the circular loop what should be the radius if initial height is $5 m$