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Work, Power & Energy

227 Questions Start Allen Test
All Exams Allen Advance Errorless
Q51 Allen 2. Dynamics of Circular Motion MCQ
A long horizontal rod has a bead which can slide along its length and is initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with a constant angular acceleration, $\alpha$ . If the coefficient of friction between the rod and bead is $\mu$ , and gravity is neglected, then the time after which the bead starts slipping is:-
A.
$\sqrt{\frac{\mu}{\alpha}}$
B.
$\frac{\mu}{\sqrt{\alpha}}$
C.
$\frac{1}{\sqrt{\mu\alpha}}$
D.
Infinitesimal
Q52 Allen 2. Dynamics of Circular Motion MCQ
A car is moving along a circular track with tangential acceleration of magnitude $a_{0}$ . It just start to slip at speed $v_{0}$ then find radius of circle. (Coefficient of friction is $\mu$ )
A.
$\frac{v_{0}^{2}}{\sqrt{(\mu g)^{2} + a_{0}^{2}}}$
B.
$\frac{v_{0}^{2}}{\sqrt{(\mu g)^{2} - a_{0}^{2}}}$
C.
$\frac{v_{0}^{2}}{\sqrt{(\mu g)^{2} - 2a_{0}^{2}}}$
D.
$\frac{v_{0}^{2}}{\sqrt{(\mu g)^{2} + 2a_{0}^{2}}}$
Q53 Allen 2. Dynamics of Circular Motion MCQ
A bead is constrained to move on rod in gravity free space as shown in figure. The rod is rotating with angular velocity $\omega$ and angular acceleration $\alpha$ about its end. If $\mu$ is coefficient of friction. Mark the correct option. (Rod rotates in the plane of paper)
A.
If $\mu = \frac{\omega^2}{\alpha}$ friction on bead is static in nature
B.
If $\mu > \frac{\omega^2}{\alpha}$ friction on bead is kinetic in nature
C.
If $\mu < \frac{\omega^2}{\alpha}$ friction is static
D.
If bead does not slide relative to rod. Friction will not exist between bead and rod.
Q54 Allen 2. Dynamics of Circular Motion MCQ
A horizontal turn table is initially at rest. It starts to rotate in horizontal plane with constant angular acceleration $3 \, rad/s^{2}$ . A block of mass $1 \, kg$ is placed 1 metre away from the axis of rotation on the turn table. A horizontal force $F = 5t \, N$ where t is in seconds, is acting on the block always towards the center of rotation. The block begins to slip at t = 1s. The coefficient of friction between block and turn table is
A.
0.2
B.
0.3
C.
0.4
D.
0.5
Q55 Allen 3. Work MCQ
A cricket player throws a ball straight upward in the air. It rises and falls back to the hands of the player. During the catch, his hands are displaced downward a few inches as the ball slows down, then.
A.
During the catch while the ball is in hand and is moving downward, the work done by the player on the ball is positive.
B.
During the throw work done by gravity is positive.
C.
During the throw while ball is in hand and moving upward, work done by ball on hand is negative.
D.
During the catch while the ball is in hand and moving downward, work done by hand plus gravity on the ball is positive.
Q56 Allen 3. Work MCQ
A force of magnitude of 30 N acting along $\hat{i} + \hat{j} + \hat{k}$ , displaces a particle from point (2, 4, 1) m to (3, 5, 2) m. The work done during this displacement is :-
A.
90 J
B.
30 J
C.
$30\sqrt{3}J$
D.
$30/\sqrt{3}J$ .
Q57 Allen 3. Work MCQ
A rope is used to lower vertically a block of mass M by a distance x with a constant downward acceleration g/2. The work done by the rope on the block is:
A.
Mgx
B.
$\frac{1}{2}$ Mgx $^{2}$
C.
$-\frac{1}{2}$ Mgx
D.
Mgx $^{2}$
Q58 Allen 3. Work MCQ
A block of mass 10 kg is released from the top of smooth wedge (whose inclination at Īø = 37Ā°) which is moving with a constant velocity 10 m/s. The work done by the force applied by wedge on the block in 2 sec will be (in joules) :-
A.
1600
B.
960
C.
Zero
D.
720
Q59 Allen 3. Work MCQ
In the figure shown find work done by tension in string on 3 kg block in first two second, from beginning of motion. The system is set free at t = 0 ( $g = 10 \, m/s^{2}$ ) (Assume pulley and string is ideal)
A.
-96 Joule
B.
-48 Joule
C.
+24 Joule
D.
96 Joule
Q60 Allen 3. Work MCQ
Force acting on a particle is $(2\hat{i} + 3\hat{j})$ N. Work done by this force is zero, when a particle is moved on the line $3y + kx = 5$ . Here value of k is
A.
2
B.
4
C.
6
D.
8
Q61 Allen 3. Work MCQ
A particle is moved from $(0,0)$ to $(a,a)$ under a force from $\vec{F}=\left(3\hat{i}+4\hat{j}\right)$ two paths. Path 1 is OP and path 2 is OQP. Let $W_{1}$ and $W_{2}$ be the work done by this force in these two paths. Then:
A.
$W_{1} = W_{2}$
B.
$W _ {1} = 2 W _ {2}$
C.
$W _ {2} = 2 W _ {1}$
D.
$W_{2} = 4W_{1}$
Q62 Allen 3. Work MCQ
The components of a force acting on a particle are varying according to the graphs shown. To reach at point B (8, 20, 0) from point A(0, 5, 12) the particle moves on paths parallel to x-axis then y-axis and then z-axis, then work done by this force is :-
A.
$192J$
B.
$58J$
C.
250 J
D.
125 J
Q63 Allen 3. Work MCQ
The work done by the force $\vec{F} = x^{2}\hat{i} + y^{2}\hat{j}$ around the path shown in the figure is
A.
$\frac{2}{3} a^{3}$
B.
zero
C.
$a^{3}$
D.
$\frac{4}{3} a^{3}$
Q64 Allen 3. Work MCQ
By applying a force $\vec{F}=(3xy-5z)\hat{j}-4\hat{k}$ a particle is moved along the path $y=x^{2}$ from point $(0,0,0)$ to the point $(2,4,0)$ . The work done by the F on the particle is :-
A.
$\frac{280}{5}$
B.
$\frac{140}{5}$
C.
$\frac{232}{5}$
D.
$\frac{192}{5}$
Q65 Allen 4. Kinetic Energy MCQ
A man who is running has half the kinetic energy of the boy of half his mass. The man speeds up by 1 m/s and then has the same kinetic energy as the boy. The original speed of the man was
A.
$\sqrt{2}$ m/s
B.
$(\sqrt{2}-1)$ m/s
C.
2 m/s
D.
$(\sqrt{2}+1)$ m/s
Q66 Allen 5. Work Energy Theorem MCQ
A body of mass 0.5 kg travels in a straight line with velocity $v = ax^{3/2}$ 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
A.
1.5 J
B.
50 J
C.
10 J
D.
100 J
Q67 Allen 5. Work Energy Theorem MCQ
In a shotput event an athlete throws the shotput of mass 10 kg with an initial speed of 1m/s at $45^{\circ}$ from a height 1.5 m above ground. Assuming air resistance to be negligible and acceleration due to gravity to be $10\ m/s^{2}$ , the kinetic energy of the shotput when it just reaches the ground will be
A.
2.5 J
B.
5.0 J
C.
52.5 J
D.
155.0 J
Q68 Allen 5. Work Energy Theorem MCQ
In the figure, a block slides along a track from one level to a higher level, by moving through an intermediate valley. The track is frictionless until the block reaches the higher level. There a frictional force stops the block in a distance d. The block's initial speed $v_{0}$ is 6 m/s, the height difference h is 1.1m and the coefficient of kinetic friction $\mu$ is 0.6. The value of d is
A.
1.17 m
B.
1.71 m
C.
7.11 m
D.
11.7 m
Q69 Allen 5. Work Energy Theorem MCQ
A small object with mass $m = 2 \, kg$ is attached to the free end of an ideal spring with $k = 10 \, Nm^{-1}$ . The other end of the spring is connected to a fixed frictionless pivot located at the origin $O$ as shown in the Figure. The relaxed length of the spring is $1 \, m$ . An unspecified force $F$ carries the object at rest from point $A$ to point $B$ . At point $B$ , the object has the speed $5 \, ms^{-1}$ . The work done by the force $F$ is (Neglect gravity):-
A.
$130 \, J$
B.
$80 \, J$
C.
$-105 \, J$
D.
$-80 \, J$
Q70 Allen 5. Work Energy Theorem MCQ
In the arrangement shown a block of mass 2kg is pressed against a spring which is compressed by 10 cm and is applying a force of 80 N to the block. The spring is not attached to the block. The coefficient of friction is 0.5. When the block is released it moves up the plane by some distance and then comes back down. The kinetic energy of the block just before it starts compressing the spring again is
A.
$2J$
B.
$1.6J$
C.
$0.8J$
D.
$0.4J$
Q71 Allen 5. Work Energy Theorem MCQ
A block of mass 10kg is attached to a relaxed spring. Other end is attached to ceiling and block is released keeping the spring in vertical position. The spring is such that it has elongation of 10 cm under a force of 100 N. The maximum velocity of block in subsequent motion is:-
A.
1 m/s
B.
1.5 m/s
C.
2.0 m/s
D.
2.5 m/s
Q72 Allen 5. Work Energy Theorem MCQ
A light spring of length 20 cm and force constant 2 N/cm is placed vertically on a table. A small block of mass 1 kg falls on it. The length h from the surface of the table at which the block will have the maximum velocity is:
A.
20 cm
B.
15 cm
C.
10 cm
D.
5cm
Q73 Allen 5. Work Energy Theorem MCQ
In the figure shown, the system is released from rest. Find the velocity of block A when block B has fallen a distance ' $\ell'$ . Assume all pulleys to be massless and frictionless.
A.
$\sqrt{\frac{g\ell}{5}}$
B.
$\sqrt{g\ell}$
C.
$\sqrt{5g\ell}$
D.
None of these
Q74 Allen 5. Work Energy Theorem Match the Columns
Two blocks, of masses M and 2M, are connected to a light spring of spring constant K that has one end fixed, as shown in figure. The horizontal surface and the pulley are frictionless. The blocks are released from rest when the spring is non deformed. The string is light.
Column-IColumn-II
(A)I and IV
(B)I and II
(C)III and IV
(D)None of these
(I)Maximum extension in the spring is $\frac{4Mg}{K}$
(II)Maximum kinetic energy of the system is $\frac{2M^{2}g^{2}}{K}$ .
(III)Maximum extension in the spring is $\frac{2Mg}{K}$ .
(IV)Maximum kinetic energy of the system is $\frac{4M^{2}g^{2}}{K}$ . Then which of the following option is correct?
Q75 Allen 6. Potential Energy MCQ
A radial force $\vec{F} = \frac{A}{r^2}\hat{r}$ acts on a particle. The work done by the force in displacing a particle from (1, 0) to (3, 4) is:
A.
$\frac{A}{5}$
B.
$\frac{A}{2}$
C.
$\frac{4A}{5}$
D.
$\frac{4A}{3}$