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Work Power and Energy

125 Questions Start Objective Test
All Exams Allen Objective Errorless
Q76 Objective 1. Taking it together MCQ
Given that the displacement of the body (in metre) is a function of time as follows $x = 2t^{4} + 5$ The mass of the body is 2 kg. What is the increase in its kinetic energy one second after the start of motion?
A.
8 J
B.
16 J
C.
32 J
D.
64 J
Q77 Objective 1. Taking it together MCQ
An object of mass m is tied to a string of length L and a variable horizontal force is applied on it which starts at zero and gradually increases until the string makes an angle $\theta$ with the vertical. Work done by the force F is
A.
mgL (1 - sin $\theta$ )
B.
mgL
C.
mgL (1 - cos $\theta$ )
D.
mgL (1 + cos $\theta$ )
Q78 Objective 1. Taking it together MCQ
A body is attached to the lower end of a vertical spiral spring and it is gradually lowered to its equilibrium position. This stretches the spring by a length d. If the same body attached to the same spring is allowed to fall suddenly, what would be the maximum stretching in this case?
A.
d
B.
2d
C.
3d
D.
(1/2)d
Q79 Objective 1. Taking it together MCQ
Kinetic energy of a particle moving in a straight line varies with time t as $K = 4t^{2}$ . The force acting on the particle
A.
is constant
B.
is increasing
C.
is decreasing
D.
first increases and then decreases
Q80 Objective 1. Taking it together MCQ
Three particles A, B and C are projected from the top of a tower with the same speed. A is thrown straight upwards, B straight down and C horizontally. They hit the ground with speeds $v_{A}$ , $v_{B}$ and $v_{C}$ , then which of the following is correct?
A.
$v_{A} = v_{B} > v_{C}$
B.
$v_{A} = v_{B} = v_{C}$
C.
$v_{A} > v_{B} = v_{C}$
D.
$v_{B} > v_{C} > v_{A}$
Q81 Objective 1. Taking it together MCQ
A particle is moving in a conservative force field from point A to point B. $U_{A}$ and $U_{B}$ are the potential energies of the particle at points A and B; and $W_{C}$ is the work done by conservative forces in the process of taking the particle from A and B. Which of the following is true?
A.
$W_{C} = U_{B} - U_{A}$
B.
$W_{C} = U_{A} - U_{B}$
C.
$U_{A} > U_{B}$
D.
$U_{B} > U_{A}$
Q82 Objective 1. Taking it together MCQ
Power supplied to a particle of mass 2 kg varies with time as $P = \frac{3t^{2}}{2}$ W. Here, t is in second. If particle is rest at t = 0, then velocity of particle at time t = 2 s will be
A.
$1 \, ms^{-1}$
B.
$4 \, ms^{-1}$
C.
$2 \, ms^{-1}$
D.
$2\sqrt{2} \, ms^{-1}$
Q83 Objective 1. Taking it together MCQ
An open knife edge of mass m is dropped from a height h on a wooden floor. If the blade penetrates up to the depth d into the wood, the average resistance offered by the wood to the knife edge is
A.
$mg\left(1+\frac{h}{d}\right)$
B.
$mg\left(1+\frac{h}{d}\right)^{2}$
C.
$mg\left(1-\frac{h}{d}\right)$
D.
$mg\left(1+\frac{d}{h}\right)$
Q84 Objective 1. Taking it together MCQ
If v be the instantaneous velocity of the body dropped from the top of a tower, when it is located at height h, then which of the following remains constant?
A.
$gh + v^{2}$
B.
$gh + \frac{v^{2}}{2}$
C.
$gh - \frac{v^{2}}{2}$
D.
$gh - v^{2}$
Q85 Objective 1. Taking it together MCQ
A block of mass 1 kg slides down a rough inclined plane of inclination $60^{\circ}$ starting from its top. If coefficient of kinetic friction is 0.5 and length of the plane d = 2 m, then work done against friction is
A.
2.45 J
B.
4.9 J
C.
9.8 J
D.
19.6 J
Q86 Objective 1. Taking it together MCQ
A raindrop falling from a height h above ground, attains a near terminal velocity when it has fallen through a height $(3/4)h$ . Which of the diagrams shown in figure correctly shows the change in kinetic and potential energy of the drop during its fall up to the ground? [NCERT Exemplar]
A.
B.
C.
D.
Q87 Objective 1. Taking it together MCQ
In a shotput event, an athlete throws the shotput of mass 10 kg with an initial speed of $1 \, ms^{-1}$ at $45^{\circ}$ from a height 1.5 m above ground. Assuming air resistance to be negligible and acceleration due to gravity to be $10 \, ms^{-2}$ , the kinetic energy of the shotput when it just reaches the ground will be
A.
2.5 J
B.
5 J
C.
52.5 J
D.
155 J
Q88 Objective 1. Taking it together MCQ
A block of mass m is attached to two unstretched springs of spring constants k, each as shown. The block is displaced towards right through a distance x and is released. The speed of the block as it passes through the mean position will be
A.
$x\sqrt{\frac{m}{2k}}$
B.
$x\sqrt{\frac{2k}{m}}$
C.
$x\sqrt{\frac{m}{k}}$
D.
$x\frac{2k}{m}$
Q89 Objective 1. Taking it together MCQ
A particle of mass 1 g executes an oscillatory motion on the concave surface of a spherical dish of radius 2m placed on a horizontal plane. If the motion of the particle begins from a point on the dish at a height of 1 cm from the horizontal plane, the total distance covered by the particle before it comes to rest, is (Curved surface is smooth and $\mu = 0.01$ for horizontal surface)
A.
2 cm
B.
10 cm
C.
1 cm
D.
20 cm
Q90 Objective 1. Taking it together MCQ
The net work done by the tension in the figure when the bigger block of mass M touches the ground is
A.
$+Mgd$
B.
$-(M + m)gd$
C.
$-mgd$
D.
zero
Q91 Objective 1. Taking it together MCQ
A block $A$ of mass $M$ rests on a wedge $B$ of mass $2M$ and inclination $\theta$ . There is sufficient friction between $A$ and $B$ , so that $A$ does not slip on $B$ . If there is no friction between $B$ and ground, the compression in spring is
A.
$\frac{Mg\cos\theta}{k}$
B.
$\frac{Mg\cos\theta\sin\theta}{k}$
C.
$\frac{Mg\sin\theta}{k}$
D.
zero
Q92 Objective 1. Taking it together MCQ
The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with the above spring of half the length, the line OA will
A.
shift towards F-axis
B.
shift towards X-axis
C.
remain as it is
D.
become double in length
Q93 Objective 1. Taking it together MCQ
A motor drives a body along a straight line with a constant force. The power P developed by the motor must vary with time t as
A.
B.
C.
D.
Q94 Objective 1. Taking it together MCQ
A force F acting on a body depends on its displacement s as $F \propto s^{-1/3}$ . The power delivered by F will depend on displacement as
A.
$s^{2/3}$
B.
$s^{-5/3}$
C.
$s^{1/2}$
D.
$s^{0}$
Q95 Objective 1. Taking it together MCQ
The force acting on a body moving along X-axis varies with the position of the particle as shown in the figure. The body is in stable equilibrium at
A.
$x = x_{1}$
B.
$x = x_{2}$
C.
Both $x_{1}$ and $x_{2}$
D.
Neither $x_{1}$ nor $x_{2}$
Q96 Objective 1. Taking it together MCQ
A body of mass 0.5 kg travels in a straight line with velocity $v = a x^{3/2}$ , where $a = 5 m^{-1/2} s^{-1}$ . The work done by the net force during its displacement from x = 0 to x = 2 m is [NCERT Exemplar]
A.
1.5 J
B.
50 J
C.
10 J
D.
100 J
Q97 Objective 1. Taking it together MCQ
The figure shows a particle sliding on a frictionless track, which terminates in a straight horizontal section. If the particle starts slipping from the point A, how far away from the track will the particle hit the ground?
A.
1m
B.
2m
C.
3m
D.
4m
Q98 Objective 1. Taking it together MCQ
A uniform chain has a mass M and length L. It is placed on a frictionless table with length $l_{0}$ hanging over the edge. The chain begins to slide down. Then, the speed v with which the end slides down from the edge is given by
A.
$v = \sqrt{\frac{g}{L}(L + l_{0})}$
B.
$v = \sqrt{\frac{g}{L}(L - l_{0})}$
C.
$v = \sqrt{\frac{g}{L}(L^{2} - l_{0}^{2})}$
D.
$v = \sqrt{2g(L - l_{0})}$
Q99 Objective 1. Taking it together MCQ
A bead of mass 1/2 kg starts from rest from A to B move in a vertical plane along a smooth fixed quarter ring of radius 5 m, under the action of a constant horizontal force F = 5 N as shown in figure. The speed of bead as it reaches the point B is (Take, $g = 10 \, ms^{-2}$ )
A.
$14.14\mathrm{ms}^{-1}$
B.
$7.07\mathrm{ms}^{-1}$
C.
$5\mathrm{ms}^{-1}$
D.
$25\mathrm{ms}^{-1}$
Q100 Objective 1. Taking it together MCQ
A car of mass m is accelerating on a level smooth road under the action of a single force F. The power delivered to the car is constant and equal to P. If the velocity of the car at an instant is v, then after travelling how much distance will it become double?
A.
$\frac{7mv^3}{3P}$
B.
$\frac{4mv^3}{3P}$
C.
$\frac{mv^3}{P}$
D.
$\frac{18mv^3}{7P}$