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Work, Power & Energy

769 Questions Start Allen Test
All Exams Allen Advance Errorless
Q401 Allen Kinematics of Circular Motion MSQ
Let $\vec{v}(t)$ be the velocity of a particle at time t. Then :
A.
$|d\vec{v}(t) / dt|$ and $d|\vec{v}(t)| / dt$ are always equal
B.
$|d\vec{v}(t)/dt|$ and $d|\vec{v}(t)|/dt$ may be equal
C.
$d|\vec{v}(t)| / dt$ can be zero while $|d\vec{v}(t) / dt|$ is not zero
D.
$d| \vec{v}(t)| / dt \neq 0$ implies $|d\vec{v}(t) / dt| \neq 0$
Q402 Allen Kinematics of Circular Motion MSQ
A particle is in motion on the x-axis. The variation of its velocity with position is as shown. The graph is circle and its equation is $x^{2} + v^{2} = 1$ , where x is in m and v in m/s. The CORRECT statement(s) is/are :-
A.
When x is positive, acceleration is negative.
B.
When x is negative, acceleration is positive.
C.
At Q, acceleration has magnitude $\frac{1}{\sqrt{2}}$ m/s $^{2}$
D.
At S, acceleration is infinite.
Q403 Allen Kinematics of Circular Motion MSQ
Two bodies A and B are moving with same constant speed v in clockwise direction in a horizontal circle of radius R and are initially diametrically opposite. The particle B now achieves a tangential acceleration $a \, m/s^{2}$ . Then which option is/are correct?
A.
they collide after time $\sqrt{\frac{\pi R}{a}}$
B.
they collide after time $\sqrt{\frac{2\pi R}{a}}$
C.
relative velocity just before collision is $\sqrt{\pi a R}$
D.
relative velocity just before collision is $\sqrt{2\pi aR}$
Q404 Allen Kinematics of Circular Motion MSQ
An ant travels along a long rod with a constant velocity relative to the rod starting from the origin. The rod is kept initially along the positive x-axis. At t = 0, the rod also starts rotating with an angular velocity $\omega$ (anticlockwise) in x-y plane about origin. Then
A.
the position of the ant at any time t is $\vec{r}=ut\left[\cos\omega t\hat{i}+\sin\omega t\hat{j}\right]$
B.
the speed of the ant at any time t is $u\sqrt{1+\omega^{2}t^{2}}$
C.
the magnitude of the tangential acceleration of the ant at any time t is $\frac{\omega^{2}tu}{\sqrt{1+\omega^{2}t^{2}}}$
D.
the speed of the ant at any time t is $\sqrt{1+2\omega^{2}t^{2}u}$
Q405 Allen Dynamics of Circular Motion MSQ
In the shown figure inside a fixed hollow cylinder with vertical axis a pendulum is rotating in a conical path with its axis same as that of the cylinder with uniform angular velocity. Radius of cylinder is 30 cm, length of string is 50 cm and mass of bob is 400 gm. The bob makes contact with the inner frictionless wall of the cylinder while moving :-
A.
The minimum value of angular velocity of the bob so that it does not leave contact is 5 rad/s
B.
Tension in the string is 5 N for all values of angular velocity
C.
For angular velocity of 10 rad/s the bob pushes the cylinder with a force of 9 N
D.
For angular velocity of 10 rad/s, tension in the string is 20N
Q406 Allen Dynamics of Circular Motion MSQ
A particle P of mass m is attached to a vertical axis by two strings AP and BP of length l each. The separation AB = l. P rotates around the axis with an angular velocity $\omega$ . The tensions in the two strings are $T_{1}$ and $T_{2}$
A.
$T_{1} = T_{2}$
B.
$T_{1} + T_{2} = m\omega^{2}l$
C.
$T_{1} - T_{2} = 2mg$
D.
$BP$ will remain taut only if $\omega \geq \sqrt{\frac{2g}{\ell}}$
Q407 Allen Dynamics of Circular Motion MSQ
On a circular turn table rotating about its center horizontally with uniform angular velocity $\omega$ rad/s placed two blocks of mass 1 kg and 2 kg, on a diameter symmetrically about center. Their separation is 1m and friction is sufficient to avoid slipping. The spring between them as shown is stretched and applied force of 5N. If $f_{1}$ and $f_{2}$ are values of friction on 1 kg and 2kg block respectively:-
A.
For $\omega = 2\mathrm{rad} / s, f_{1} = 3N$ and $f_{2} = 1N$
B.
For $\omega = 3\mathrm{rad} / s, f_{1} = 0.5N$ and $f_{2} = 4N$
C.
For $\omega = \sqrt{10}$ rad/s, $f_{1} = 0$ and $f_{2} = 5N$
D.
For $\omega = \sqrt{10}$ rad/s, $f_{1} = 0$ and $f_{2} = 0N$
Q408 Allen 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 $^{2}$
Q409 Allen 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)
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
Q410 Allen 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
Q411 Allen 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.
Q412 Allen 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.
Q413 Allen 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.
Q414 Allen 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
Q415 Allen 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.
$\vec{F}=\frac{3(yi+x\hat{j})}{(x^{2}+y^{2})^{3/2}}$
Q416 Allen 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.
Q417 Allen 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
Q418 Allen 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
Q419 Allen 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.
Q420 Allen 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.
Q421 Allen 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.
Q422 Allen 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
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.
$-\frac{1}{2}mga_{0}t_{0}^{2}$
Q423 Allen 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 :-
A.
zero
B.
$-Na_{0}t_{0}^{2}$
C.
$\frac{Na_{0}t^{2}}{2}$
D.
None of these
Q424 Allen 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
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.
$-\frac{1}{2}mga_{0}t_{0}^{2}$
Q425 Allen 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
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