Work, Power & Energy
769 Questions
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JEE (Main) April 2024
Q26
Errorless
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
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
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
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
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
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) 2023
Q32
Allen
JEE Main PYQ
MCQ
A body of mass 200g is tied to a spring of spring constant 12.5 N/m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5 rad/s, then the ratio of extension in the spring to its natural length will be:
A.
1 : 2
B.
1 : 1
C.
2 : 3
D.
2 : 5
JEE (Main) 2023
Q33
Allen
JEE Main PYQ
Numerical
A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of 54 km/hr is $t(1 - e^{-\pi/2})$ s. The value of t is ____.
Correct Answer: 40
Explanation:
Ans. (40)
$v \frac {d v}{d x} = \frac {v ^ {2}}{R} \Rightarrow \int_ {1 5} ^ {v} \frac {d v}{v} = \frac {1}{R} \int_ {0} ^ {x} d x$
$v = 1 5 e ^ {x / R}$
$\frac {d x}{d t} = 1 5 e ^ {x / R}$
$\int_ {0} ^ {\frac {\pi x}{2}} e ^ {- x / R} d x = 1 5 \int_ {0} ^ {t _ {0}} d t$
$t _ {0} = 4 0 \left(1 - e ^ {- \pi / 2}\right)$
$v \frac {d v}{d x} = \frac {v ^ {2}}{R} \Rightarrow \int_ {1 5} ^ {v} \frac {d v}{v} = \frac {1}{R} \int_ {0} ^ {x} d x$
$v = 1 5 e ^ {x / R}$
$\frac {d x}{d t} = 1 5 e ^ {x / R}$
$\int_ {0} ^ {\frac {\pi x}{2}} e ^ {- x / R} d x = 1 5 \int_ {0} ^ {t _ {0}} d t$
$t _ {0} = 4 0 \left(1 - e ^ {- \pi / 2}\right)$
JEE (Main) 2023
Q34
Allen
JEE Main PYQ
Numerical
A body of mass 1 kg begins to move under the action of a time dependent force $\vec{F} = (t\hat{i} + 3t^2\hat{j})N$ . where $\hat{i}$ and $\hat{j}$ are the unit vectors along $x$ and $y$ axis. The power developed by above force, at the time $t = 2s$ . will be ____W.
Correct Answer: 100
Explanation:
Ans. (100)
$\vec {F} = t \hat {i} + 3 t ^ {2} \hat {j}$
$\frac {m d \vec {v}}{d t} = t \hat {i} + 3 t ^ {2} \hat {j}$
$m = 1 k g, \int_ {0} ^ {\vec {v}} d v = \int_ {0} ^ {t} t d t \hat {i} + \int_ {0} ^ {t} 3 t ^ {2} d t \hat {j}$
$\vec {v} = \frac {t ^ {2}}{2} \hat {i} + t ^ {3} \hat {j}$
$\mathrm{Power} = \vec {F} \cdot \vec {V} = \frac {t ^ {3}}{2} + 3 t ^ {5}$
$\mathrm{At} t = 2, \mathrm{power} = \frac {8}{2} + 3 \times 3 2 = 1 0 0$
$\vec {F} = t \hat {i} + 3 t ^ {2} \hat {j}$
$\frac {m d \vec {v}}{d t} = t \hat {i} + 3 t ^ {2} \hat {j}$
$m = 1 k g, \int_ {0} ^ {\vec {v}} d v = \int_ {0} ^ {t} t d t \hat {i} + \int_ {0} ^ {t} 3 t ^ {2} d t \hat {j}$
$\vec {v} = \frac {t ^ {2}}{2} \hat {i} + t ^ {3} \hat {j}$
$\mathrm{Power} = \vec {F} \cdot \vec {V} = \frac {t ^ {3}}{2} + 3 t ^ {5}$
$\mathrm{At} t = 2, \mathrm{power} = \frac {8}{2} + 3 \times 3 2 = 1 0 0$
JEE (Main) 2023
Q35
Allen
JEE Main PYQ
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 in zero.
(E) Work done by the air resistance on an oscillating pendulum in 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 in zero.
(E) Work done by the air resistance on an oscillating pendulum in 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) Jan. 2023
Q36
Errorless
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
Q37
Errorless
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
Q38
Errorless
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
Q39
Errorless
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
Q40
Errorless
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
Q41
Errorless
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
Q42
Errorless
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
Q43
Errorless
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.
$d / h_{1} = 2\sqrt{3}$
2022
Q44
Allen
JEE Main PYQ
MCQ
A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is $\frac{K}{\pi}$ rev./min. The value of K is:
(Assume the string is massless and unstretchable)
(JEE (Main) 2022)
A.
400
B.
300
C.
600
D.
800
JEE (Main) 2022
Q45
Allen
JEE Main PYQ
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) 2022
Q46
Allen
JEE Main PYQ
MCQ
A particle experiences a variable force $\vec{F} = (4x\hat{\imath} + 3y^2\hat{j})$ in a horizontal $x-y$ plane. Assume distance in meters and force in newton. If the particle moves from point (1, 2) to point (2, 3) in the $x-y$ plane, the Kinetic Energy changes by
A.
$50.0 J$
B.
$12.5 J$
C.
$25.0 J$
D.
$0 J$
JEE (Main) 2022
Q47
Allen
JEE Main PYQ
Numerical
A ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at the top of vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{h}{2}$ . The spring constant is ____ $Nm^{-1}$ . (Use $g = 10 ms^{-2}$ )
Correct Answer: 120
Explanation:
Ans. (120)
By energy conservation
$P E = K E$
$m g \left(H + \frac {H}{2}\right) = \frac {1}{2} k x ^ {2} \left(x = \frac {H}{2}\right)$
$0.1 0 0 \times 1 0 \times \frac {3}{2} (0.1 0) = \frac {1}{2} k (0.0 5 \times 0.0 5)$
$k = \frac {3 \times 0.1 0}{0.0 5 \times 0.0 5} = \frac {3 \times 1 0 0 0}{2 5} = 1 2 0 N / m$
By energy conservation
$P E = K E$
$m g \left(H + \frac {H}{2}\right) = \frac {1}{2} k x ^ {2} \left(x = \frac {H}{2}\right)$
$0.1 0 0 \times 1 0 \times \frac {3}{2} (0.1 0) = \frac {1}{2} k (0.0 5 \times 0.0 5)$
$k = \frac {3 \times 0.1 0}{0.0 5 \times 0.0 5} = \frac {3 \times 1 0 0 0}{2 5} = 1 2 0 N / m$
JEE (Main) June 2022
Q48
Errorless
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
Q49
Errorless
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
Q50
Errorless
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.
$\left(\frac{B}{2A}\right)^{\frac{1}{5}}$