Work, Power & Energy
238 Questions
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JEE (Main) April 2024
Q26
Errorless
7. Critical Thinking
MCQ
A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to
A.
$t^{2}$
B.
$t^{2/3}$
C.
$t^{3/2}$
D.
t
JEE (Main) April 2024
Q27
Errorless
7. Critical Thinking
MCQ
A bullet of mass 50 g is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is
A.
32%
B.
44%
C.
16%
D.
84%
JEE (Main) April 2024
Q28
Errorless
7. Critical Thinking
MCQ
When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be
A.
$500\%$
B.
$600\%$
C.
$6\%$
D.
$60\%$
JEE (Main) April 2024
Q29
Errorless
7. Critical Thinking
MCQ
A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is
A.
$\sqrt{6} m$
B.
$2m$
C.
$1m$
D.
$\sqrt{5} m$
JEE (Advanced) 2024
Q30
Errorless
9. JEE Section
Numerical
Two particles, 1 and 2, each of mass m, are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their centre of mass at $x_{0}$ , are oscillating with amplitude a and angular frequency $\omega$ . Thus, their positions at time t are given by $x_{1}(t) = (x_{0} + d) + a \sin \omega t$ and $x_{2}(t) = (x_{0} - d) - a \sin \omega t$ , respectively, where d > 2a. Particle 3 of mass m moves towards this system with speed $u_{0} = a \omega / 2$ , and undergoes instantaneous elastic collision with particle 2, at time $t_{0}$ . Finally, particles 1 and 2 acquire a centre of mass speed $v_{cm}$ and oscillate with amplitude b and the same angular frequency $\omega$ .
.
If the collision occurs at time $t_{0}=0$ , the value of $v_{cm}/(\alpha\omega)$ will be ____
.
If the collision occurs at time $t_{0}=0$ , the value of $v_{cm}/(\alpha\omega)$ will be ____
Correct Answer: 0.75
Explanation:
At $T$ , $t_0 = 0$
$V _ {C M} = \frac {m . \frac {a \omega}{2} + m . a \omega}{m + m}$
$V _ {C M} = \frac {3 a \omega}{4} \Rightarrow \frac {V _ {C M}}{a \omega} = \frac {3}{4} \Rightarrow \frac {V _ {C M}}{a \omega} = 0. 7 5.$
$V _ {C M} = \frac {m . \frac {a \omega}{2} + m . a \omega}{m + m}$
$V _ {C M} = \frac {3 a \omega}{4} \Rightarrow \frac {V _ {C M}}{a \omega} = \frac {3}{4} \Rightarrow \frac {V _ {C M}}{a \omega} = 0. 7 5.$
JEE (Advanced) 2024
Q31
Errorless
9. JEE Section
Numerical
Two particles, 1 and 2, each of mass m, are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their centre of mass at $x_{0}$ , are oscillating with amplitude a and angular frequency $\omega$ . Thus, their positions at time t are given by $x_{1}(t) = (x_{0} + d) + a \sin \omega t$ and $x_{2}(t) = (x_{0} - d) - a \sin \omega t$ , respectively, where d > 2a. Particle 3 of mass m moves towards this system with speed $u_{0} = a \omega / 2$ , and undergoes instantaneous elastic collision with particle 2, at time $t_{0}$ . Finally, particles 1 and 2 acquire a centre of mass speed $v_{cm}$ and oscillate with amplitude b and the same angular frequency $\omega$ .
If the collision occurs at time $t_{0}=\pi/(2\omega)$ , then the value of $4b^{2}/a^{2}$ , will be ____
If the collision occurs at time $t_{0}=\pi/(2\omega)$ , then the value of $4b^{2}/a^{2}$ , will be ____
Correct Answer: 4.25
Explanation:
$t_0 = \frac{\pi}{2\omega} = \frac{T}{4}$
Particles are at extreme position
$\text { extension } = 2 a$
After collision
aĻ/2
In C-frame
$\begin{array}{c} \bullet \xrightarrow {} a \omega / 4 \\ \bullet \xrightarrow {} a \omega / 4 \end{array} \xrightarrow {} a \omega / 4$
$\text { extension } = 2 b \quad \text { extreme }$
Using WET,
$W _ {\text { spring }} = \Delta K. E.$
$\frac {1}{2} k (2 b) ^ {2} - \frac {1}{2} k (2 a) ^ {2} = 2 \times \frac {1}{2} m \times \left(\frac {a \omega}{4}\right) ^ {2}$
(k=spring constant)
$4 k b ^ {2} - 4 k a ^ {2} = 2 \times m \times \frac {a ^ {2}}{1 6} \times \frac {2 k}{m}$
$4 b ^ {2} = \frac {1 7}{4} a ^ {2} \Rightarrow \frac {4 b ^ {2}}{a ^ {2}} = 4.2 5.$
Particles are at extreme position
$\text { extension } = 2 a$
After collision
aĻ/2
In C-frame
$\begin{array}{c} \bullet \xrightarrow {} a \omega / 4 \\ \bullet \xrightarrow {} a \omega / 4 \end{array} \xrightarrow {} a \omega / 4$
$\text { extension } = 2 b \quad \text { extreme }$
Using WET,
$W _ {\text { spring }} = \Delta K. E.$
$\frac {1}{2} k (2 b) ^ {2} - \frac {1}{2} k (2 a) ^ {2} = 2 \times \frac {1}{2} m \times \left(\frac {a \omega}{4}\right) ^ {2}$
(k=spring constant)
$4 k b ^ {2} - 4 k a ^ {2} = 2 \times m \times \frac {a ^ {2}}{1 6} \times \frac {2 k}{m}$
$4 b ^ {2} = \frac {1 7}{4} a ^ {2} \Rightarrow \frac {4 b ^ {2}}{a ^ {2}} = 4.2 5.$
JEE (Main) Jan. 2023
Q32
Errorless
7. Critical Thinking
MCQ
As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball Q of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball Q after collision will be $(g = 10m/s^{2})$
A.
0
B.
0.25 m/s
C.
2 m/s
D.
4 m/s
JEE (Main) Jan. 2023
Q33
Errorless
7. Critical Thinking
MCQ
Identify the correct statements from the following
(A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative.
(B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.
(C) Work done by friction on a body sliding down an inclined plane is positive.
(D) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero.
(E) Work done by the air resistance on an oscillating pendulum is negative.
Choose the correct answer from the options given below
(A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative.
(B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.
(C) Work done by friction on a body sliding down an inclined plane is positive.
(D) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero.
(E) Work done by the air resistance on an oscillating pendulum is negative.
Choose the correct answer from the options given below
A.
B and E only
B.
A and C only
C.
B, D and E only
D.
B and D only
JEE (Main) April 2023
Q34
Errorless
7. Critical Thinking
MCQ
Two bodies are having kinetic energies in the ratio 16:9. If they have same linear momentum, the ratio of their masses respectively is
A.
4:3
B.
3:4
C.
16:9
D.
9:16
JEE (Main) April 2023
Q35
Errorless
7. Critical Thinking
MCQ
A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. After collision, they stick together and continue to move together with velocity
A.
v
B.
$\frac{v}{2}$
C.
$\frac{v}{3}$
D.
$\frac{v}{4}$
JEE (Main) April 2023
Q36
Errorless
7. Critical Thinking
MCQ
Given below are two statements :
Statement I : A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance.
Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero.
In the light of the above statements,
choose the most appropriate answer from the options given below
A.
If both assertion and reason are true and the reason is the correct explanation of the assertion.
B.
If both assertion and reason are true but reason is not the correct explanation of the assertion.
C.
If assertion is true but reason is false.
D.
If the assertion and reason both are false.
E.
If assertion is false but reason is true.
JEE (Main) April 2023
Q37
Errorless
7. Critical Thinking
MCQ
A bullet of mass 0.1 kg moving horizontally with speed $400 \, ms^{-1}$ hits a wooden block of mass 3.9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block and the surface is ____
(Given $g = 10 \, ms^{2}$ )
A.
0.50
B.
0.90
C.
0.65
D.
0.25
JEE (Main) April 2023
Q38
Errorless
7. Critical Thinking
MCQ
The ratio of powers of two motors is $\frac{3\sqrt{x}}{\sqrt{x}+1}$ , that are capable of raising 300 kg water in 5 minutes and 50 kg water in 2 minutes respectively from a well of 100 m deep. The value of x will be
A.
2
B.
4
C.
2.4
D.
16
JEE (Advanced) 2023
Q39
Errorless
9. JEE Section
MSQ
A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height 3h from the ground, as shown in the figure. A spherical ball of mass m is released on the slide from rest at a height h from the top of the terrace. The ball leaves the slide with a velocity $\vec{u}_{0}=u_{0}\hat{x}$ and falls on the ground at a distance d from the building making an angle $\theta$ with the horizontal. It bounces off with a velocity $\vec{v}$ and reaches a maximum height $h_{1}$ . The acceleration due to gravity is g and the coefficient of restitution of the ground is $1/\sqrt{3}$ . Which of the following statement(s) is(are) correct
A.
$\vec{u}_0 = \sqrt{2gh}\hat{x}$
B.
$\vec{v} = \sqrt{2gh} (\hat{x} -\hat{z})$
C.
$\theta = 60^{\circ}$
D.
$d / h_{1} = 2\sqrt{3}$
JEE (Main) June 2022
Q40
Errorless
7. Critical Thinking
MCQ
A particle experiences a variable force $\vec{F} = (4x\hat{i} + 3y^2\hat{j})$ in a horizontal $x - y$ plane. Assume distance in meters and force is newton. If the particle moves from point (1, 2) to point (2, 3) in the $x - y$ plane, the kinetic energy changes by
A.
$50.0J$
B.
$12.5J$
C.
$25.0J$
D.
$0J$
JEE (Main) June 2022
Q41
Errorless
7. Critical Thinking
MCQ
In the given figure, the block of mass m is dropped from the point 'A'. The expression for kinetic energy of block when it reaches point 'B' is
Ground
Ground
A.
$\frac {1}{2} m g y _ {0} ^ {2}$
B.
$\frac {1}{2} m g y ^ {2}$
C.
$m g (y - y _ {0})$
D.
$mgy_0$
JEE (Main) June 2022
Q42
Errorless
7. Critical Thinking
MCQ
Potential energy as a function of r is given by $U = \frac{A}{r^{10}} - \frac{B}{r^{5}}$ , where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be
A.
$\left(\frac{A}{B}\right)^{\frac{1}{5}}$
B.
$\left(\frac{B}{A}\right)^{\frac{1}{5}}$
C.
$\left(\frac{2A}{B}\right)^{\frac{1}{5}}$
D.
$\left(\frac{B}{2A}\right)^{\frac{1}{5}}$
JEE (Main) June 2022
Q43
Errorless
7. Critical Thinking
MCQ
What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass (Assume the collision to be head-on elastic collision)
A.
$50.0\%$
B.
$66.6\%$
C.
$55.5\%$
D.
$33.3\%$
JEE (Main) June 2022
Q44
Errorless
7. Critical Thinking
MCQ
A particle of mass 500 gm is moving in a straight line with velocity $v = bx^{5/2}$ . The work done by the net force during its displacement from x = 0 to x = 4m is (Take $b = 0.25 m^{-3/2} s^{-1}$ )
A.
2 J
B.
4 J
C.
8 J
D.
16 J
JEE (Main) June 2022
Q45
Errorless
7. Critical Thinking
MCQ
A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as $a = k^{2}rt^{2}$ . Where k is a constant. The power delivered to the particle by the force acting on it is given as
A.
Zero
B.
$mk^{2}r^{2}t^{2}$
C.
$mk^{2}r^{2}t$
D.
$mk^{2}rt$
JEE (Main) July 2022
Q46
Errorless
7. Critical Thinking
MCQ
A bullet of mass $200g$ having initial kinetic energy $90J$ is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to $40J$ within 1s, the minimum length of the pool, the bullet has to travel so that it completely comes to rest is
A.
45 m
B.
90 m
C.
125 m
D.
25 m
JEE (Main) July 2022
Q47
Errorless
7. Critical Thinking
MCQ
A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed $10 \, ms^{-1}$ gets embedded in it, then loss of kinetic energy will be
A.
4.9 J
B.
9.8 J
C.
14.7 J
D.
19.6 J
JEE (Main) July 2022
Q48
Errorless
7. Critical Thinking
MCQ
As per the given figure, two blocks each of mass 250g are connected to a spring of spring constant $2Nm^{-1}$ . If both are given velocity v in opposite directions, then maximum elongation of the spring is
A.
$\frac{v}{2\sqrt{2}}$
B.
$\frac{v}{2}$
C.
$\frac{v}{4}$
D.
$\frac{v}{\sqrt{2}}$
JEE (Main) July 2022
Q49
Errorless
7. Critical Thinking
MCQ
A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be
A.
1:1
B.
2:1
C.
1:4
D.
4:1
JEE (Main) July 2022
Q50
Errorless
7. Critical Thinking
MCQ
If momentum of a body is increased by 20%, then its kinetic energy increases by
A.
36%
B.
40%
C.
44%
D.
48%