Physics - Work Energy Power - Quiz-5

A particle of mass m is driven by a machine that delivers a constant power of k watts. If the particle starts from rest the force on the particle at time t is:

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$\sqrt{(\frac{m k}{2})} t^{- 1 / 2}$
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$\sqrt{(m k)} t^{- 1 / 2}$
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$\sqrt{(2 m k)} t^{- 1 / 2}$
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$\frac{1}{2} \sqrt{(m k)} t^{- 1 / 2}$

Two particles of masses m₁,m₂ move with initial velocities u₁ and u₂. On collision, one of the particles get excited to higher level, after absorbing energy $ε$ . If final velocities of particles be v₁ and v₂, then we must have
(a)m₁²u₁+m₂²u₂- $ε$ =m₁²v₁+m₂²v₂
(b) $\frac{1}{2}$ m₁u₁²+ $\frac{1}{2}$ m₂u₂= $\frac{1}{2}$ m₁v₁²+ $\frac{1}{2}$ m₂v₂²- $ε$
(c) $\frac{1}{2}$ m₁u₁²+ $\frac{1}{2}$ m₂u₂²- $ε$ = $\frac{1}{2}$ m₁v₁²+ $\frac{1}{2}$ m₂v₂²
(d) $\frac{1}{2}$ m₁²u₁²+ $\frac{1}{2}$ m₂²u₂²+ $ε$ = $\frac{1}{2}$ m₁²v₁²+ $\frac{1}{2}$ m₂²v₂²

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A ball is thrown vertically downwards from a height of 20 m with an initial velocity v_o. It collides with the ground, loses 50% of its energy in a collision and rebounds to the same height. The initial velocity v_o is: (Take g = 10 ms^-2)

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14 ms^-1
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20 ms^-1
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28 ms^-1
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10 ms^-1

On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle θ to its initial direction and has a speed v/3. The second block's speed after the collision is:
(1)2√2v/3

(2)3v/4

(3)3v/√2

(4)√3v/2

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A uniform force of (3i + j) N acts on a particle of mass 2 kg. Hence the particle is displaced from position (2i+k) m to position (4i+3j-k) m. The work done by the force on the particle is-

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9J
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6J
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13J
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15J

The potential energy of a system increases if work is done

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by the system against a conservative force
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by the system against a nonconservative force
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upon the system by a conservative force
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upon the system by a nonconservative force

Force F on a particle moving in a straight line varies with distance d as shown in the figure. The work done on the particle during its displacement of 12 m is

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() 21 J
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() 26 J
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() 13 J
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() 18 J

An engine pumps water through a hosepipe. Water passes through the pipe and leaves it with a velocity of 2 $m s^{- 1} .$ The mass per unit length of water in the pipe is 100 $k g m^{- 1} .$ What is the power of the engine?

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400 W
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200 W
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100 W
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800 W

A particle of mass M starting from rest undergoes uniform acceleration. If the speed acquired in time T is v, the power delivered to the particle is

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$\frac{{Mv}^{2}}{T}$
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$\frac{1}{2} \frac{{Mv}^{2}}{T^{2}}$
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$\frac{{Mv}^{2}}{T^{2}}$
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$\frac{1}{2} \frac{{Mv}^{2}}{T}$

A body of mass 1 kg is thrown upwards with a velocity $20 {ms}^{- 1} .$ It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction? $(g = 10 {ms}^{- 2})$

(a) 20 J (b) 30 J

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A block of mass M is attached to the lower end of a vertical spring. The spring is hung from the ceiling and has a force constant value of k. The mass is released from rest with the spring initially unstretched. The maximum extension produced along the length of the spring will be:

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Mg/k
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2Mg/k
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4 Mg/k
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Mg/2k

The points of maximum and minimum attraction in the curve between potential energy (U) and distance (r) of a diatomic molecules are respectively -

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S and R
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T and S
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R and S
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S and T

K is the force constant of a spring. The work done in increasing its extension from $l_{1}$ to $l_{2}$ will be

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$K (l_{2} - l_{1})$
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$\frac{K}{2} (l_{2} + l_{1})$
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$K (l_{2}^{2} - l_{1}^{2})$
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$\frac{K}{2} (l_{2}^{2} - l_{1}^{2})$

An electron is accelerated through a potential difference of 200 volts. If e/m for the electron be $1.6 \times 10^{11}$ coulomb/kg, the velocity acquired by the electron will be

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$8 \times 10^{6} m / s$
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$8 \times 10^{5} m / s$
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$5.9 \times 10^{6} m / s$
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$5.9 \times 10^{5} m / s$

Consider a drop of rainwater having a mass of 1gm falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take 'g' constant with a value 10 m/s². The work done by the
(i) gravitational force and the
(ii) resistive force of air is:

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(i) 1.25 J (ii) -8.25 J
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(i) 100 J (ii) 8.75 J
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(i) 10 J (ii) -8.75 J
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(i) -10 J (ii) -8.75 J

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 AB = D. The height h is equal to :-

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$\frac{3}{2} D$
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D
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$\frac{7}{4} D$
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$\frac{5}{4} D$

A body of mass 1 kg begins to move under the action of a time-dependent force

\vec{F} = (2 t \hat{i} + 3 t^{2} \hat{j}) N

, where

\hat{i}

and

\hat{j}

are unit vectors along the X and Y-axis. What power will be developed by the force at the time (t)?

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(2t² + 4t⁴) W
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(2t³ + 3t³) W
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(2t³ + 3t⁵) W
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(2t³ + 3t⁴) W

Q. 17 Which of the diagrams in the figure correctly shows the change in kinetic energy of an iron sphere falling freely in a lake having sufficient density to impart it a terminal velocity?

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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?

1 . \sqrt{2 g R} 2 . \sqrt{3 g R} 3 . \sqrt{5 g R} 4 . \sqrt{g R}

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Two similar springs P and Q have spring constants k_P and k_Q, such that k_P> k_Q. They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springs W_Pand W_Q are related as, in case (a) and case (b), respectively.

_{$1 . W_{P} = W_{Q}; W_{P} > W_{Q} 2 . W_{P} = W_{Q}; W_{P} = W_{Q} 3 . W_{P} > W_{Q}; W_{P} < W_{Q} 4 . W_{P} < W_{Q}; W_{P} < W_{Q}$}

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A particle of mass m is driven by a machine that delivers a constant power of k watts. If the particle starts from rest, the force on the particle at time t is:

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$\sqrt{\frac{m k}{2}} t^{\frac{- 1}{2}}$
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$\sqrt{m k} t^{\frac{- 1}{2}}$
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$\sqrt{2 m k} t^{\frac{- 1}{2}}$
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$\frac{1}{2}$ $\sqrt{m k} t^{\frac{- 1}{2}}$

Two particles of masses m₁ and m₂ move with initial velocities u₁ and u₂ respectively. On collision, one of the particles gets excited to a higher level, after absorbing energy E. If the final velocities of particles are v₁ and v₂, then we must have:

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$m_{1}^{2} u_{1} + m_{2}^{2} u_{2} - E = m_{1}^{2} v_{1} + m_{2}^{2} v_{2}$
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$\frac{1}{2} m_{1} u_{1}^{2} + \frac{1}{2} m_{2} u_{2}^{2} = \frac{1}{2} m_{1} v_{1}^{2} + \frac{1}{2} m_{2} v_{2}^{2}$
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$\frac{1}{2} m_{1} u_{1}^{2} + \frac{1}{2} m_{2} u_{2}^{2} - E = \frac{1}{2} m_{1} v_{1}^{2} + \frac{1}{2} m_{2} v_{2}^{2}$
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$\frac{1}{2} m_{1}^{2} u_{1}^{2} + \frac{1}{2} m_{2}^{2} u_{2}^{2} + E = \frac{1}{2} m_{1}^{2} v_{1}^{2} + \frac{1}{2} m_{2}^{2} v_{2}^{2}$

A uniform force of

(3 \hat{i} + \hat{j})

newton acts on a particle of mass 2 kg. Hence the particle is displaced from position

(2 \hat{i} + \hat{k})

meter to position

(4 \hat{i} + 3 \hat{j} - \hat{k})

meter. The work done by the force on the particle is:

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6 J
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13 J
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15 J
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9 J

A body projected vertically from the earth reaches a height equal to earth’s radius before returning to the earth. The power exerted by the gravitational force:

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is greatest at the instant just before the body hits the earth.
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remains constant throughout.
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is greatest at the instant just after the body is projected.
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is greatest at the highest position of the body.

The potential energy of a system increases if work is done

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by the system against a conservative force
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by the system against a non-conservative force
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upon the system by a conservative force
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upon the system by a non-conservative force

Force F on a particle moving in a straight line varies with distance d as shown in the figure. The work done on the particle during its displacement of 12 m is:

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21 J
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26 J
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13 J
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18 J

A body of mass 1 kg is thrown upwards with a velocity 20 ms^-1. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction? (g =10 ms^-2)

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20 J
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30 J
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40 J
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10 J

An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?

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$\frac{1}{2} m v^{3}$
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$m v^{3}$
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$\frac{1}{2} m v^{2}$
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$\frac{1}{2} m^{2} v^{2}$

Water falls from a height of 60 m at a rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine? (g = 10 m/s²)

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8.1 kW
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10.2 kW
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12.3 kW
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7.0 kW

A vertical spring with a force constant k is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d. The net work done in the process is:

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$m g (h + d) + \frac{1}{2} k d^{2}$
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$m g (h + d) - \frac{1}{2} k d^{2}$
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$m g (h - d) - \frac{1}{2} k d^{2}$
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$m g (h - d) + \frac{1}{2} k d^{2}$

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Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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