A particle with total mechanical energy which is small and negative is under the influence of a one dimensional potential U x = x 4 4 - x 2 2 J , where x is in meters. At time t = 0 s , it is at x = - 0 . 5 m . Then at a later time it can be found,

between x = - 1 . 0 m to x = 0 . 0 m

between x = - 1 . 0 m to x = 1 . 0 m

between x = 0 . 0 m to x = 1 . 0 m

Both kinetic energy and potential energy

Match the following? Column-I Column-II (a) F net (i) d K d t (b) F cons (ii) Δ U + Δ K (c) ∑ W non-cons (iii) - d U d x (d) Power (iv) d P d t

(a-iii), (b-ii), (c-ii), (d-ii)

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A stone is thrown upwards as shown in the diagram. When it reaches P, the energy of the stone will be maximum.

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Important Questions on Effect of Energy: Work, Power and Energy

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Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

The potential energy function for a two dimensional force is given by

U = 3 x^{3} y - 7 x

. The force that acts at the point

(x, y)

is (Take

\hat{i}

and

\hat{j}

as unit vectors along

X

- and

Y

- axes)

HARD

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

A particle is moving in a circle of radius

r

under the action of a force

F = α r^{2}

which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy

= 0

for

r = 0

EASY

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

A block of mass

100 g

moving at a speed of

2 m s^{- 1}

compresses a spring through a distance

2 cm

before its speed is halved. Find the spring constant of the spring

EASY

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

A particle of mass

m

moves in a circular orbit under the central potential field,

U (r) = \frac{- C}{r}

, where

C

is a positive constant. The correct radius - velocity graph of the particle's motion is :

EASY

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

A rod of length

l

and mass

m

fixed at one end, is hanging vertically. The other end is now raised so that the rod makes an angle

30 °

with horizontal line. The work done in the process will be :

MEDIUM

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

The graphs below show the magnitude of the force on a particle as it moves along the positive $X$ -axis from the origin to $X = X_{1}$ . The force is parallel to the $X$ -axis and conservative. The maximum magnitude $F_{1}$ has the same value for all graphs. Rank the situations according to the change in the potential energy associated with the force, least (or most negative) to greatest (or most positive).

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MEDIUM

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

A particle with total mechanical energy which is small and negative is under the influence of a one dimensional potential

U (x) = \frac{x^{4}}{4} - \frac{x^{2}}{2} J

, where

x

is in meters. At time

t = 0 s

, it is at

x = - 0.5 m

. Then at a later time it can be found,

MEDIUM

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

Which of the following is not a correct statement?

EASY

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

Flying birds has

MEDIUM

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

Ratio of potential energies of body A and body B will be

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EASY

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

Two equal masses are attached to two each of a spring of spring constant

k

. The masses are pulled out symmetrically to stretch the spring by a length

x

over is natural length. The work done by the spring on each mass is

EASY

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

Write in your words the definition of potential energy.

EASY

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

The potential energy of a particle varies with distance

' x'

as shown in the graph. The force acting on the particle is zero at
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Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

A particle is released from a height

H

. At a certain height its kinetic energy is half of its potential energy with reference to the surface of the earth. Height and speed of the particle at that instant are respectively

EASY

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

The potential energy of a particle in a central field has the form

U (r) = \frac{1}{r^{2}} - \frac{1}{r},

where

' r'

is the distance from the centre of the field. The magnitude of the maximum attractive force in Newton is

MEDIUM

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

A particle of mass

m

moves under the influence of the potential

V (x) = P / x^{2} - Q / x

. Here

P, Q

are real positive constants. The angular frequency of small oscillations of the particle around the equilibrium point is

MEDIUM

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

Match the following?

Column-I		Column-II
(a)	$F_{net}$	(i)	$\frac{d K}{d t}$
(b)	$F_{cons}$	(ii)	$Δ U + Δ K$
(c)	$\sum W_{non-cons}$	(iii)	$\frac{- d U}{d x}$
(d)	$Power$	(iv)	$\frac{d P}{d t}$

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Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

9800 J

of energy was spent to raise a mass of

70 kg

. The mass was raised to a height of _____?

HARD

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

A block of

9 kg

is moving with a velocity of

4 m / s

on a frictionless surface. The block comes to rest by compressing the spring. If the spring constant is

4 x 10^{4} N / kg

, then find the compression in the spring.

HARD

Physical Science>Physics>Effect of Energy: Work, Power and Energy>Energy

A spring of spring constant $K = 4 x 10^{3} N / m$ is compressed by $2 cm$ , then determine the potential energy stored in spring.

A stone is thrown upwards as shown in the diagram. When it reaches P, the energy of the stone will be maximum.

Important Questions on Effect of Energy: Work, Power and Energy

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