A particle is free to move along the X -axis has potential energy given by U x = k 1 - e - x 2 for - ∞ ≤ x ≤ + ∞ , where k is a positive constant of appropriate dimensions. Then:

for small displacements from x = 0 , the motion is simple harmonic.

at points away from the origin, the particle is in unstable equilibrium

for any finite non-zero value of x , there is a force directed away from the origin

if its total mechanical energy is k / 2 , it has its minimum kinetic energy at the origin

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A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy $K$ with time $t$ most appropriately? The figures are only illustrative and not to the scale.

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Alpha Question Bank for Medical: Physics>Chapter 8 - Work, Energy and Power>Exercise-4>Q 1

A body is executing simple harmonic motion. At a displacement

x

, its potential energy is

E_{1}

and at a displacement

y

, its potential energy is

E_{2}

. The potential energy

E

at a displacement

(x + y)

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Alpha Question Bank for Medical: Physics>Chapter 8 - Work, Energy and Power>Exercise-4>Q 2

A particle is free to move along the $X$ -axis has potential energy given by $U (x) = k [1 - e^{- x^{2}}]$ for $- \infty \leq x \leq + \infty$ , where $k$ is a positive constant of appropriate dimensions. Then:

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Alpha Question Bank for Medical: Physics>Chapter 8 - Work, Energy and Power>Exercise-4>Q 3

A stone of mass

1 kg

tied to a light inextensible string of length

L = \frac{10}{3} m

, is whirling in a circular path in a vertical plane. The ratio of maximum tension in the string to the minimum tension in the string is

4 .

g

is taken to be

10 m s^{- 2}

, the speed of the stone at the highest point of the circle is:

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Alpha Question Bank for Medical: Physics>Chapter 8 - Work, Energy and Power>Exercise-4>Q 4

A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles

30 °

and

60 °

from vertical (lowest position) are

T_{1}

and

T_{2}

respectively then

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Alpha Question Bank for Medical: Physics>Chapter 8 - Work, Energy and Power>Exercise-4>Q 5

A car of mass

m

starts moving so that its velocity varies according to the law

v = β \sqrt{s},

where

β

is a constant, and

s

is the distance covered. The total work performed by all the forces which are acting on the car during the first

t

seconds after the beginning of motion is

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Alpha Question Bank for Medical: Physics>Chapter 8 - Work, Energy and Power>Exercise-4>Q 6

A block of mass

250 g

is kept on a vertical spring of spring constant

100 N m^{- 1}

fixed from below. The spring is now compressed to have a length

10 cm

shorter than its natural length and the system is released from this position. How high does the block rise? Take

g = 10 m s^{- 2} .

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Alpha Question Bank for Medical: Physics>Chapter 8 - Work, Energy and Power>Exercise-4>Q 7

In a projectile motion,

K E

varies with time as in graph:

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Alpha Question Bank for Medical: Physics>Chapter 8 - Work, Energy and Power>Exercise-4>Q 8

The force acting on a body moving along $x$ -axis varies with the position of the particle as shown in the figure.

Question Image

The body is in stable equilibrium at

Important Questions on Work, Energy and Power

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