A particle 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 point 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

Physics - Work Energy Power - Quiz-3

If a body of mass 200 g falls from a height 200 m and its total P.E. is converted into K.E. at the point of contact of the body with earth surface, then what is the decrease in P.E. of the body at the contact (g = 10 m/s²)

0%

200 J
0%

400 J
0%

600 J
0%

900 J

If momentum is increased by 20%, then K.E. increases by

0%

44%
0%

55%
0%

66%
0%

77%

The kinetic energy of a body of mass 2 kg and momentum of 2 Ns is

0%

1 J
0%

2 J
0%

3 J
0%

4 J

The decrease in the potential energy of a ball of mass 20 kg which falls from a height of 50 cm is

0%

968 J
0%

98 J
0%

1980 J
0%

None of these

A 0.5 kg ball is thrown up with an initial speed 14 m/s and reaches a maximum height of 8.0m. How much energy is dissipated by air drag acting on the ball during the ascent

0%

19.6 Joule
0%

4.9 Joule
0%

10 Joule
0%

9.8 Joule

An ice cream has a marked value of 700 kcal. How many kilowatt- hour of energy will it deliver to the body as it is digested

0%

0.81 kWh
0%

0.90 kWh
0%

1.11 kWh
0%

0.71 kWh

A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by 1m/s so as to have same K.E. as that of the boy. The original speed of the man will be

0%

$\sqrt{2} m / s$
0%

$(\sqrt{2} - 1) m / s$
0%

$\frac{1}{(\sqrt{2} - 1)} m / s$
0%

$\frac{1}{\sqrt{2}} m / s$

A particle of mass m at rest is acted upon by a force F for a time t. Its Kinetic energy after an interval t is

0%

$\frac{F^{2} t^{2}}{m}$
0%

$\frac{F^{2} t^{2}}{2 m}$
0%

$\frac{F^{2} t^{2}}{3 m}$
0%

$\frac{F t}{2 m}$

Two bodies of masses m and 4 m are moving with equal K.E. The ratio of their linear momentums is

0%

4 : 1
0%

1 : 1
0%

1 : 2
0%

1 : 4

A particle of mass m₁ is moving with a velocity v₁ and another particle of mass m₂ is moving with a velocity v₂. Both of them have the same momentum but their different kinetic energies are E₁ and E₂ respectively. If m₁ > m₂ then

0%

E₁ < E₂
0%

$\frac{E_{1}}{E_{2}} = \frac{m_{1}}{m_{2}}$
0%

E₁ > E₂
0%

E₁ = E₂

Four particles are given, having same momentum. Which one has maximum kinetic energy-

0%

Proton
0%

Electron
0%

Deutron
0%

α-particles

A block of mass m initially at rest is dropped from a height h on to a spring of force constant k. The maximum compression in the spring is x then-

0%

$m g h = \frac{1}{2} k x^{2}$
0%

$m g (h + x) = \frac{1}{2} k x^{2}$
0%

$m g h = \frac{1}{2} k {(x + h)}^{2}$
0%

$m g (h + x) = \frac{1}{2} k {(x + h)}^{2}$

A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It slides down a smooth surface to the ground, then climbs up another hill of height 30 m and finally slides down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is:

0%

10 m/s
0%

$10 \sqrt{30}$ m/s
0%

40 m/s
0%

20 m/s

The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant K and compresses it by length L. The maximum momentum of the block after collision is

0%

Zero
0%

$\frac{M L^{2}}{K}$
0%

$\sqrt{M K} L$
0%

$\frac{K L^{2}}{2 M}$

A body of mass m accelerates uniformly from rest to v₁ in time t₁. As a function of time t, the instantaneous power delivered to the body is

0%

$\frac{m v_{1} t}{t_{1}}$
0%

$\frac{m v_{1}^{2} t}{t_{1}}$
0%

$\frac{m v_{1} t^{2}}{t_{1}}$
0%

$\frac{m v_{1}^{2} t}{t_{1}^{2}}$

A weight lifter lifts 300 kg from the ground to a height of 2 meter in 3 second. The average power generated by him is

0%

5880 watt
0%

4410 watt
0%

2205 watt
0%

1960 watt

The average power required to lift a 100 kg mass through a height of 50 metres in approximately 50 seconds would be

0%

50 J/s
0%

5000 J/s
0%

100 J/s
0%

980 J/s

A 60 kg man runs up a staircase in 12 seconds while a 50 kg man runs up the same staircase in 11, seconds, the ratio of the rate of doing their work is

0%

6 : 5
0%

12 : 11
0%

11 : 10
0%

10 : 11

What average horsepower is developed by an 80 kg man while climbing in 10 s a flight of stairs that rises 6 m vertically

0%

0.63 HP
0%

1.26 HP
0%

1.8 HP
0%

2.1 HP

A quarter horse-power motor runs at a speed of 600 r.p.m. Assuming 40% efficiency, the work done by the motor in one rotation will be:

0%

7.46 J
0%

7400 J
0%

7.46 ergs
0%

74.6 J

An engine pumps up 100 kg of water through a height of 10 m in 5 s. Given that the efficiency of the engine is 60% . If g = 10 ms^–2, the power of the engine is

0%

3.3 kW
0%

0.33 kW
0%

0.033 kW
0%

33 kW

An engine pump is used to pump a liquid of density ρ continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is

0%

$\frac{1}{2} A ρ v^{3}$
0%

$\frac{1}{2} A ρ v^{2}$
0%

$\frac{1}{2} A ρ v$
0%

$A ρ v$

Two equal masses, m₁ and m₂ , moving in the same straight line at velocities +3 m/s and –5 m/s respectively, collide elastically. Their velocities after the collision will be:

0%

+4 m/s for both
0%

–3 m/s and +5 m/s
0%

4. –5 m/s and +3 m/s
0%

3. –4 m/s and +4 m/s

A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on the table is:

0%

MgL
0%

MgL/3
0%

MgL/9
0%

MgL/18

If W₁, W₂ and W₃ represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W₁, W₂ and W₃

0%

W₁ > W₂ > W₃
0%

W₁ = W₂ = W₃
0%

W₁ < W₂ < W₃
0%

W₂ > W₁ > W₃

The displacement x of a particle moving in one dimension under the action of a constant force is related to the time t by the equation $t = \sqrt{x} + 3$ , where x is in meters and t is in seconds. The work done by the force in the first 6 seconds is

0%

9 J
0%

6 J
0%

0 J
0%

3 J

A force $F = - k (y i + x j)$ (where k is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the force on the particle is:

0%

$- 2k a^{2}$
0%

$2k a^{2}$
0%

$-k a^{2}$
0%

$ka^2$

A lorry and a car moving with the same K.E. are brought to rest by applying the same retarding force, then:

0%

Lorry will come to rest in a shorter distance
0%

Car will come to rest in a shorter distance
0%

Both will come to rest in a same distance
0%

None of the above

A particle 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

0%

At point away from the origin, the particle is in unstable equilibrium
0%

For any finite non-zero value of x, there is a force directed away from the origin
0%

If its total mechanical energy is k/2, it has its minimum kinetic energy at the origin
0%

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

The kinetic energy acquired by a mass m in travelling a certain distance d starting from rest under the action of a constant force is directly proportional to

0%

$\sqrt{m}$
0%

Independent of m
0%

$1 / \sqrt{m}$
0%

m

0:0:1

0:0:1

Practice Physics Quiz Questions and Answers

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