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Work, Power & Energy

769 Questions Start Allen Test
All Exams Allen Advance Errorless
Q351 Allen Kinematics of Circular Motion MCQ
A particle is projected with initial velocity 50m/sec making an angle of $53^{\circ}$ with horizontal. Find the radius of curvature of particle when velocity of particle is perpendicular to the direction of its initial velocity:
A.
175.8 m
B.
200.3 m
C.
165.6 m
D.
170.8 m
Q352 Allen Kinematics of Circular Motion MCQ
A particle starts from rest and performing circular motion of constant radius with speed given by $v = \alpha \sqrt{x}$ where $\alpha$ is a constant and x is the distance covered. The correct graph of magnitude of its tangential acceleration ( $a_{t}$ ) and centripetal acceleration ( $a_{c}$ ) versus t will be:
A.
B.
C.
D.
Q353 Allen Kinematics of Circular Motion MCQ
A particle is moving in a circular path. The acceleration and momentum of the particle at a certain moment are $\vec{a}=(4\hat{i}+3\hat{j})m/s^{2}$ and $\vec{p}=(8\hat{i}-6\hat{j})kg-m/s$ . The motion of the particle is
A.
uniform circular motion
B.
accelerated circular motion
C.
de-accelerated circular motion
D.
can not say anything with $\vec{a}$ and $\vec{p}$ only
Q354 Allen Kinematics of Circular Motion MCQ
A point P moves in counter clockwise direction on a circular path as shown in the figure. The movement of 'P' is such that it sweeps out a length $s = t^{2} + 5$ , where s is in metres and t is in seconds. The radius of the path is 20 m. The acceleration of 'P' when $t = 5\sqrt{\frac{3}{10}}$ seconds is nearly:
A.
$2m / s^2$
B.
$1.5m / s^2$
C.
$2.5m / s^2$
D.
$3m / s^2$
Q355 Allen Dynamics of Circular Motion MCQ
A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane, it follows that-
A.
Its velocity is constant
B.
Its acceleration is constant
C.
Its kinetic energy is constant
D.
It moves in a straight line
Q356 Allen Dynamics of Circular Motion MCQ
A particle of mass m is tied to a light string and rotated with a speed v along a circular path of radius r. If T = tension in the string and mg = gravitational force on the particle then the actual forces acting on the particle are :
A.
mg and T only
B.
mg, T and an additional force of $\frac{mv^{2}}{r}$ directed inwards.
C.
$mg, T$ and an additional force of $\frac{mv^2}{r}$ directed outwards.
D.
only a force $\frac{mv^2}{r}$ directed outwards.
Q357 Allen Dynamics of Circular Motion MCQ
An unbanked circular highway curve on level ground makes a turn of $90^{\circ}$ . The highway carries traffic at $108 km-hr^{-1}$ , and the centripetal force on a vehicle is not to exceed 1/10 of its weight. What is the minimum length of the curve?
A.
1.4 km
B.
1 km
C.
0.6 km
D.
1.7 km
Q358 Allen 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
Q359 Allen 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.
$\frac{v_{0}^{2}}{\sqrt{(\mu g)^{2} + 2a_{0}^{2}}}$
Q360 Allen 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.
Q361 Allen 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
Q362 Allen 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.
Q363 Allen 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.
$30/\sqrt{3}J$ .
Q364 Allen 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 $^{2}$
Q365 Allen 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
Q366 Allen 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
Q367 Allen 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
Q368 Allen 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.
$W_{2} = 4W_{1}$
Q369 Allen 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
Q370 Allen 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.
$\frac{4}{3} a^{3}$
Q371 Allen 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.
$\frac{192}{5}$
Q372 Allen 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
Q373 Allen 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
Q374 Allen 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
Q375 Allen 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