Work, Power & Energy
227 Questions
Start Allen Test
Q101
Allen
2. Dynamics of Circular Motion
MSQ
A heavy particle is tied to the end $A$ of a string of length $1.6 \, m$ . Its other end $O$ is fixed. It revolves as a conical pendulum with the string making $60^\circ$ with the vertical. Then
A.
its period of revolution is $\frac{4\pi}{7}$ sec
B.
the tension in the string is double the weight of the particle
C.
the velocity of the particle = $2.8\sqrt{3}$ m/s
D.
the centripetal acceleration of the particle is $9.8\sqrt{3}$ m/s $^{2}$
Q102
Allen
2. Dynamics of Circular Motion
MSQ
A car is moving with constant speed on a rough banked road.
Figure shows the free body diagram of car in three situation A, B and C respectively:-
A)
B)
C)
Figure shows the free body diagram of car in three situation A, B and C respectively:-
A)
B)
C)
A.
Car in A has more speed than car in C
B.
Car in A has less speed than car in B
C.
FBD for car in A is not possible
D.
If $\mu > \tan \theta$ the $FBD$ for car $C$ is not possible
Q103
Allen
3. Work
MSQ
Which of the following statements is TRUE for a system comprising of two bodies in contact exerting frictional force on each other :
A.
total work done by static friction on whole system is always zero.
B.
work done by static friction on a body is always zero
C.
work done by kinetic friction on a body is always negative
D.
total work done by internal kinetic friction on whole system is always negative
Q104
Allen
5. Work Energy Theorem
MSQ
Select the correct alternatives :-
A.
Work energy theorem can be applied in non-inertial frame of reference also.
B.
Work done by any force can be positive, negative or zero depends on choice of reference frame.
C.
Kinetic friction force always acts opposite to direction of velocity.
D.
Work done by a force is independent of the choice of reference frame.
Q105
Allen
5. Work Energy Theorem
MSQ
A body of mass 'm' is moving slowly up the rough hill from point A to point B as shown in figure by a force which is acting tangential to surface at each point on the hill. Work done by this force is :
A.
Independent of shape of trajectory.
B.
Independent of horizontal component of displacement.
C.
Depends on coefficient of friction between the surfaces.
D.
Depends on the mass of the body.
Q106
Allen
5. Work Energy Theorem
MSQ
In figure, a block of mass m is released from rest when spring was in its natural length. The pulley also has mass m but it is frictionless. Suppose the value of m is such that finally it is just able to lift the block of mass 2kg up after being released. Mark the correct statement (s) :-
A.
Mass of m required to just lift 2kg block is 2kg.
B.
The tension in the rod, when m has zero acceleration is 20N.
C.
The normal force acting on 2 kg block when m has zero acceleration is 10N.
D.
The tension in the string when displacement of m is maximum possible is 20N.
Q107
Allen
5. Work Energy Theorem
MSQ
Block A of mass 1 kg is kept on block B of mass 2kg which is kept on smooth surface as shown in figure. At t = 0 both blocks are at rest and a force of 6N is applied on block B. Friction coefficient between A and B is 0.5. Which of the following is/are correct :-
A.
Acceleration of both the blocks is $2m/s^{2}$
B.
Work done by friction (in ground frame) on A is zero from t = 0 to t = 2 sec
C.
Friction force on $A$ is $2N$
D.
Kinetic energy of A at t = 2 sec is 8J
Q108
Allen
6. Potential Energy
MSQ
Which of the following is/are conservative force(s)?
A.
$\vec{F}=2r^{3}\hat{r}$
B.
$\vec{F}=-\frac{5}{r}\hat{r}$
C.
$\vec{F}=\frac{3(x\hat{i}+y\hat{j})}{(x^{2}+y^{2})^{3/2}}$
D.
$\vec{F}=\frac{3(yi+x\hat{j})}{(x^{2}+y^{2})^{3/2}}$
Q109
Allen
6. Potential Energy
MSQ
If one of the forces acting on a particle is conservative then :
A.
Work done by this force is zero when the particle moves exactly once around any closed path.
B.
Work done by this force equals the change in the kinetic energy of the particle.
C.
It obeys Newton's second law.
D.
Work done by this force depends on the end points of the motion, not on the path in between.
Q110
Allen
6. Potential Energy
MSQ
A particle of mass 5 kg moving in the X - Y plane has its potential energy given by $U = (-7x + 24y)J$ . The particle is initially at origin and has a velocity $\vec{u} = (14.4\hat{i} + 4.2\hat{j})m/s$ .
A.
The particle has speed 25 m/s at t = 4 sec.
B.
The particle has an acceleration $25 \, m/s^{2}$
C.
The acceleration of particle is normal to its initial velocity
D.
All above are correct
Q111
Allen
7. Motion in Vertical Circle
MSQ
A particle is given a velocity at the bottom most position in a smooth spherical shell of radius 2m. It just complete a vertical circular motion. Then
A.
acceleration of particle when the velocity of the particle is in vertically upward direction is $g\sqrt{10}$
B.
acceleration of particle when the velocity of the particle is in vertically downward direction is $g\sqrt{10}$
C.
acceleration of the particle at the top most point of path is g
D.
acceleration of the particle at the bottom most point is 5 g
Q112
Allen
8. Power
MSQ
A particle of mass 2 kg is projected with an initial speed u = 10 m/sec at an angle $\theta = 30^{\circ}$ with the horizontal:
A.
Total work done on the particle during the first half of the total time of flight of the particle is $(-25) J$ .
B.
Total work done on the particle during the total time of flight of the particle is 0 J.
C.
Average power delivered to the particle during the first half of the flight is (-50) watt.
D.
The radius of curvature of the trajectory of the particle at the highest point of the projectile is 7.5m.
Q113
Allen
8. Power
MSQ
A particle is moving from point (1, 2, 3) to (4, 6, 8) with initial speed $5\sqrt{2} m/s$ on a straight line. It experiences a force of $\left(3\hat{i}+4\hat{j}\right)N$ throughout its journey. Choose the CORRECT statement(s):
A.
Initial velocity vector of the particle is $\left(3\hat{i} + 4\hat{j} + 5\hat{k}\right)m / s$
B.
Work done by the given force in the journey is $25J\left(W = \vec{F}.\vec{S}\right)$
C.
Initial power delivered by the given force is 25 watt ( $P = \vec{F}.\vec{V}$ , P is power and V is velocity)
D.
If velocity of the particle doesn't change there must be some other force acting on the particle.
Q114
Allen
8. Power
MSQ
A particle is subjected to a conservative force as seen in the graphs, which of the following are correct.
A.
Particle is in stable equilibrium at point 3 and b.
B.
Particle is in neutral equilibrium at point b and 2.
C.
No power is delivered by the force to the particle at 1, 3, and b.
D.
Particle has maximum kinetic energy at position b.
Q115
Allen
3. Work
MCQ
Comprehension Passage:
A block of mass m is kept in an elevator which starts moving downward with an acceleration $a_{0}$ as shown in figure. The block is observed by two observers A and B for a time interval $t_{0}$ .
The observer B finds that the work done by gravity is
The observer B finds that the work done by gravity is
A.
$\frac{1}{2}mg^{2}t_{0}^{2}$
B.
$-\frac{1}{2}mg^{2}t_{0}^{2}$
C.
$\frac{1}{2}mga_{0}t_{0}^{2}$
D.
$-\frac{1}{2}mga_{0}t_{0}^{2}$
Q116
Allen
3. Work
MCQ
Comprehension Passage:
A block of mass m is kept in an elevator which starts moving downward with an acceleration $a_{0}$ as shown in figure. The block is observed by two observers A and B for a time interval $t_{0}$ .
The observer B finds that work done by normal reaction N is :-
The observer B finds that work done by normal reaction N is :-
A.
zero
B.
$-Na_{0}t_{0}^{2}$
C.
$\frac{Na_{0}t^{2}}{2}$
D.
None of these
Q117
Allen
3. Work
MCQ
Comprehension Passage:
A block of mass m is kept in an elevator which starts moving downward with an acceleration $a_{0}$ as shown in figure. The block is observed by two observers A and B for a time interval $t_{0}$ .
According to observer B, the net work done on the block is
According to observer B, the net work done on the block is
A.
$-\frac{1}{2}ma_{0}t_{0}^{2}$
B.
$\frac{1}{2}ma_{0}^{2}t_{0}^{2}$
C.
$\frac{1}{2}mga_{0}t_{0}^{2}$
D.
$-\frac{1}{2}mga_{0}t_{0}^{2}$
Q118
Allen
3. Work
MCQ
Comprehension Passage:
A block of mass m is kept in an elevator which starts moving downward with an acceleration $a_{0}$ as shown in figure. The block is observed by two observers A and B for a time interval $t_{0}$ .
According to the observer A
According to the observer A
A.
the work done by gravity is zero
B.
the work done by normal reaction is zero
C.
the work done by pseudo force is zero
D.
all the above
Q119
Allen
6. Potential Energy
MCQ
Comprehension Passage:
In the figure the variation of potential energy of a particle of mass m = 2kg is represented w.r.t. its x-coordinate. The particle moves under the effect of this conservative force along the x-axis.
If the particle is released at the origin then:
If the particle is released at the origin then:
A.
It will move towards positive x-axis.
B.
It will move towards negative x-axis.
C.
It will remain stationary at the origin.
D.
Its subsequent motion cannot be decided due to lack of information.
Q120
Allen
6. Potential Energy
MCQ
Comprehension Passage:
In the figure the variation of potential energy of a particle of mass m = 2kg is represented w.r.t. its x-coordinate. The particle moves under the effect of this conservative force along the x-axis.
If the particle is released at $x = 2 + \Delta$ where $\Delta \rightarrow 0$ (it is positive) then its maximum speed in subsequent motion will be-
If the particle is released at $x = 2 + \Delta$ where $\Delta \rightarrow 0$ (it is positive) then its maximum speed in subsequent motion will be-
A.
$\sqrt{22}$ m/s
B.
$\sqrt{25}$ m/s
C.
$\sqrt{24}$ m/s
D.
$\sqrt{23}$ m/s
Q121
Allen
6. Potential Energy
MCQ
Comprehension Passage:
In the figure the variation of potential energy of a particle of mass m = 2kg is represented w.r.t. its x-coordinate. The particle moves under the effect of this conservative force along the x-axis.
x = -5 m and x = 10 m positions of the particle are respectively of-
x = -5 m and x = 10 m positions of the particle are respectively of-
A.
Neutral and stable equilibrium
B.
Neutral and unstable equilibrium
C.
Unstable and stable equilibrium
D.
Stable and unstable equilibrium.
Q122
Allen
2. Dynamics of Circular Motion
Match the Columns
shows certain situations and shows information about forces.
Column-I
Column-I
| Column-I | Column-II | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
Front view of a car rounding a curve with constant speed.
Correct Answer: (A-P,Q), (B-P,Q,S), (C-P,Q,R), (D-P,Q,R)
Explanation:
Ans. (A-P,Q), (B-P,Q,S), (C-P,Q,R), (D-P,Q,R)
No slipping anywhere.
Net force is centripetal as v=constant.
No slipping anywhere.
Net force is centripetal as v=constant.
Q123
Allen
2. Dynamics of Circular Motion
Match the Columns
A block is placed on a horizontal table which can rotate about its axis. The block is placed at a certain distance from centre as shown in figure. Table rotates such that particle does not slide. Select possible direction of net acceleration of block at the instant shown in figure. Column-I with Column-II
| Column-I | Column-II | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
Correct Answer: (A-R), (B-S) (C-Q), (D-P)
Explanation:
Ans. (A-R), (B-S) (C-Q), (D-P)
(A) $a_{t}=0, a_{C}\neq0$ (B) $a_{t}\neq0, a_{C}\neq0$ (C) $a_{t}\neq0, a_{C}\neq0$ (D) $a_{t}\neq0, a_{C}=0 (v=0)$
(A) $a_{t}=0, a_{C}\neq0$ (B) $a_{t}\neq0, a_{C}\neq0$ (C) $a_{t}\neq0, a_{C}\neq0$ (D) $a_{t}\neq0, a_{C}=0 (v=0)$
Q124
Allen
5. Work Energy Theorem
Match the Columns
In the figure shown are two blocks A and B of same mass connected with pulley and string to each other. Initially both of them are at a height of h = 0.5 m from ground. After they are released they move in either direction and one of them strike the ground. For, the interval from releasing to when one of them strike, some physical quantities are in Column-I and their modulus values in SI units are in Column-II.
| Column-I | Column-II | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
Correct Answer: (A-Q), (B-P), (C-Q), (D-S)
Explanation:
Ans. (A-Q), (B-P), (C-Q), (D-S) $y_{A}=2y_{B}\Rightarrow v_{A}=2v_{B}$ A moves $\downarrow$ and
B moves $\uparrow$ as
Tension on B is more than A. $mgh-\frac{mgh}{2}=\frac{1}{2}mv_{A}^{2}+\frac{1}{2}mv_{B}^{2}$ $\frac{gh}{2}=\frac{5}{2}v_{B}^{2}$ $\Rightarrow v_{B}=\sqrt{\frac{5}{5}}=1, v_{A}=2$ mg-T=maA
2T-mg=maB $a_{A}=2a_{B}$
B moves $\uparrow$ as
Tension on B is more than A. $mgh-\frac{mgh}{2}=\frac{1}{2}mv_{A}^{2}+\frac{1}{2}mv_{B}^{2}$ $\frac{gh}{2}=\frac{5}{2}v_{B}^{2}$ $\Rightarrow v_{B}=\sqrt{\frac{5}{5}}=1, v_{A}=2$ mg-T=maA
2T-mg=maB $a_{A}=2a_{B}$
Q125
Allen
5. Work Energy Theorem
Match the Columns
In the given figure block of mass $m = 1/2 \, kg$ is stationary with respect to car moving with constant acceleration $a = 5 \, m/s^{2}$ . (All surfaces are smooth) Column-I with Column-II
| Column-I | Column-II | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
Correct Answer: (A-Q), (B-P), (C-Q), (D-P)
Explanation:
Ans. (A-Q), (B-P), (C-Q), (D-P)
A) $W_{N}+W_{mg}=\Delta KE$ $V_{f}=at=5\times2=10\ m/s$ $W_{N}=\frac{1}{2}mV_{f}^{2}-0=\frac{1}{2}\times\frac{1}{2}\times10^{2}=25J$
B) $W_{mg}=0$ (No horizontal displacement)
C) $W_{net}=\Delta KE=25J$
D) $W.D_{out}=0(S=0)$
A) $W_{N}+W_{mg}=\Delta KE$ $V_{f}=at=5\times2=10\ m/s$ $W_{N}=\frac{1}{2}mV_{f}^{2}-0=\frac{1}{2}\times\frac{1}{2}\times10^{2}=25J$
B) $W_{mg}=0$ (No horizontal displacement)
C) $W_{net}=\Delta KE=25J$
D) $W.D_{out}=0(S=0)$