Work, Power & Energy
769 Questions
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Q701
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 6
A ball of mass 2 kg is released from the bottom of a tank filled with water up to 2 m. On reaching the top its kinetic energy is found to be 16 J. Ignoring the viscosity and taking $g = 10 \, ms^{-2}$ , answer the following questions.
Density of the ball in $\frac{\mathrm{kg}}{\mathrm{m}^3}$ is
Density of the ball in $\frac{\mathrm{kg}}{\mathrm{m}^3}$ is
A.
$\frac{5}{7} \times 10^{3}$
B.
$\frac{3}{4} \times 10^{3}$
C.
$\frac{2}{3} \times 10^{3}$
D.
$\frac{1}{3} \times 10^{3}$
Q702
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 7
The radial component of a conservative force (like electrostatic or gravitational force) can be calculated from the potential energy function U, by using the formula $F = -\frac{dU}{dr}$ . Consider a particle bound to a certain point at a distance r from the centre of the force such that the potential energy of this particle varies with r as $U(r) = \frac{A}{r^{2}} - \frac{B}{r}$ where A and B are positive constants. Based on the above facts, answer the following questions.
For the particle, the equilibrium distance is $r_0$ . Then
A.
$r_0 = \frac{A}{B}$
B.
$r_0 = \frac{2A}{B}$
C.
$r_0 = \frac{3A}{B}$
D.
$r_0 = \frac{B}{4A}$
Q703
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 7
The radial component of a conservative force (like electrostatic or gravitational force) can be calculated from the potential energy function U, by using the formula $F = -\frac{dU}{dr}$ . Consider a particle bound to a certain point at a distance r from the centre of the force such that the potential energy of this particle varies with r as $U(r) = \frac{A}{r^{2}} - \frac{B}{r}$ where A and B are positive constants. Based on the above facts, answer the following questions.
The nature of the equilibrium
A.
is stable
B.
is unstable
C.
is neutral
D.
non-predictable, as data provided is insufficient
Q704
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 7
The radial component of a conservative force (like electrostatic or gravitational force) can be calculated from the potential energy function U, by using the formula $F = -\frac{dU}{dr}$ . Consider a particle bound to a certain point at a distance r from the centre of the force such that the potential energy of this particle varies with r as $U(r) = \frac{A}{r^{2}} - \frac{B}{r}$ where A and B are positive constants. Based on the above facts, answer the following questions.
The particle is moved from the equilibrium position to infinity. A work $W$ is done in the process. Then
A.
$W = \frac{B^2}{2A}$
B.
$W = \frac{B^2}{4A}$
C.
$W = \frac{2B^2}{A}$
D.
$W = \frac{4B^2}{A}$
Q705
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 7
The radial component of a conservative force (like electrostatic or gravitational force) can be calculated from the potential energy function U, by using the formula $F = -\frac{dU}{dr}$ . Consider a particle bound to a certain point at a distance r from the centre of the force such that the potential energy of this particle varies with r as $U(r) = \frac{A}{r^{2}} - \frac{B}{r}$ where A and B are positive constants. Based on the above facts, answer the following questions.
It is found that at a particular radial position, the total energy possessed by the particle is $E = -\frac{3B^{2}}{16A}$ . Assuming the motion to be purely radial, the velocity will be zero at position given by (in terms of equilibrium distance $r_{0}$ )
A.
$r_{0}$
B.
$\frac{r_{0}}{3}$
C.
$\frac{2r_{0}}{3}$
D.
$\frac{r_{0}}{5}$
Q706
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 8
The system is released from rest with both the springs in unstretched positions. The mass of each block is 1 kg and force constant of each spring is $10 \, Nm^{-1}$ .
Based on above information, answer the following questions.
Extension of horizontal spring, in equilibrium, is
Based on above information, answer the following questions.
Extension of horizontal spring, in equilibrium, is
A.
0.2 m
B.
0.4 m
C.
0.6 m
D.
0.8 m
Q707
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 8
The system is released from rest with both the springs in unstretched positions. The mass of each block is 1 kg and force constant of each spring is $10 \, Nm^{-1}$ .
Based on above information, answer the following questions.
Maximum speed of the block placed horizontally is
Based on above information, answer the following questions.
Maximum speed of the block placed horizontally is
A.
$1.26 \, ms^{-1}$
B.
$1.93 \, ms^{-1}$
C.
$2.21 \, ms^{-1}$
D.
$3.21 \, ms^{-1}$
Q708
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 9
The kinetic energy is the capacity of the body to do work by virtue of its motion. For a body of mass m moving with a velocity v, it is mathematically defined as $KE = \frac{1}{2}mv^{2}$ .
For conservative forces doing work, the kinetic energy always increases (or remains constant) and for non-conservative forces doing work, the kinetic energy decreases. A plot of force vs displacement is shown here. The conservative force is shown as positive and that due to non-conservative force is shown as negative. Consider a body of mass 4 kg having a velocity of $20 \, ms^{-1}$ at the origin of the coordinates. Based on the above facts and figures, answer the following questions.
The kinetic energy of the particle at the origin of the coordinates is
For conservative forces doing work, the kinetic energy always increases (or remains constant) and for non-conservative forces doing work, the kinetic energy decreases. A plot of force vs displacement is shown here. The conservative force is shown as positive and that due to non-conservative force is shown as negative. Consider a body of mass 4 kg having a velocity of $20 \, ms^{-1}$ at the origin of the coordinates. Based on the above facts and figures, answer the following questions.
The kinetic energy of the particle at the origin of the coordinates is
A.
400 J
B.
600 J
C.
800 J
D.
1000 J
Q709
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 9
The kinetic energy is the capacity of the body to do work by virtue of its motion. For a body of mass m moving with a velocity v, it is mathematically defined as $KE = \frac{1}{2}mv^{2}$ .
For conservative forces doing work, the kinetic energy always increases (or remains constant) and for non-conservative forces doing work, the kinetic energy decreases. A plot of force vs displacement is shown here. The conservative force is shown as positive and that due to non-conservative force is shown as negative. Consider a body of mass 4 kg having a velocity of $20 \, ms^{-1}$ at the origin of the coordinates. Based on the above facts and figures, answer the following questions.
The kinetic energy of the body at $B$ , $x = 4 \mathrm{~m}$ is
For conservative forces doing work, the kinetic energy always increases (or remains constant) and for non-conservative forces doing work, the kinetic energy decreases. A plot of force vs displacement is shown here. The conservative force is shown as positive and that due to non-conservative force is shown as negative. Consider a body of mass 4 kg having a velocity of $20 \, ms^{-1}$ at the origin of the coordinates. Based on the above facts and figures, answer the following questions.
The kinetic energy of the body at $B$ , $x = 4 \mathrm{~m}$ is
A.
376 J
B.
576 J
C.
776 J
D.
824 J
Q710
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 9
The kinetic energy is the capacity of the body to do work by virtue of its motion. For a body of mass m moving with a velocity v, it is mathematically defined as $KE = \frac{1}{2}mv^{2}$ .
For conservative forces doing work, the kinetic energy always increases (or remains constant) and for non-conservative forces doing work, the kinetic energy decreases. A plot of force vs displacement is shown here. The conservative force is shown as positive and that due to non-conservative force is shown as negative. Consider a body of mass 4 kg having a velocity of $20 \, ms^{-1}$ at the origin of the coordinates. Based on the above facts and figures, answer the following questions.
The kinetic energy of the body at $E$ , $x = 10 \, \mathrm{m}$ is
For conservative forces doing work, the kinetic energy always increases (or remains constant) and for non-conservative forces doing work, the kinetic energy decreases. A plot of force vs displacement is shown here. The conservative force is shown as positive and that due to non-conservative force is shown as negative. Consider a body of mass 4 kg having a velocity of $20 \, ms^{-1}$ at the origin of the coordinates. Based on the above facts and figures, answer the following questions.
The kinetic energy of the body at $E$ , $x = 10 \, \mathrm{m}$ is
A.
1036 J
B.
836 J
C.
636 J
D.
436 J
Q711
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 9
The kinetic energy is the capacity of the body to do work by virtue of its motion. For a body of mass m moving with a velocity v, it is mathematically defined as $KE = \frac{1}{2}mv^{2}$ .
For conservative forces doing work, the kinetic energy always increases (or remains constant) and for non-conservative forces doing work, the kinetic energy decreases. A plot of force vs displacement is shown here. The conservative force is shown as positive and that due to non-conservative force is shown as negative. Consider a body of mass 4 kg having a velocity of $20 \, ms^{-1}$ at the origin of the coordinates. Based on the above facts and figures, answer the following questions.
Let us assume the body to return to $O$ under the action of these forces, then the kinetic energy of the body at the origin of the coordinates will
For conservative forces doing work, the kinetic energy always increases (or remains constant) and for non-conservative forces doing work, the kinetic energy decreases. A plot of force vs displacement is shown here. The conservative force is shown as positive and that due to non-conservative force is shown as negative. Consider a body of mass 4 kg having a velocity of $20 \, ms^{-1}$ at the origin of the coordinates. Based on the above facts and figures, answer the following questions.
Let us assume the body to return to $O$ under the action of these forces, then the kinetic energy of the body at the origin of the coordinates will
A.
again be 800 J
B.
be more than 800 J
C.
be less than 800 J
D.
be greater or less than 800 J
Q712
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 10
A bob of mass 1 kg is suspended from an inextensible string of length 1 m. When the string makes an angle of $60^{\circ}$ with the vertical, speed of the bob is $4 \, ms^{-1}$ . Based on above information, answer the following questions.
Net acceleration of the bob at this instant is
A.
$10.4 \, ms^{-2}$
B.
$16 \, ms^{-2}$
C.
$18.2 \, ms^{-2}$
D.
$20.4 \, ms^{-2}$
Q713
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 10
A bob of mass 1 kg is suspended from an inextensible string of length 1 m. When the string makes an angle of $60^{\circ}$ with the vertical, speed of the bob is $4 \, ms^{-1}$ . Based on above information, answer the following questions.
The maximum height upto which the bob will rise with respect to the bottom most point is
A.
1.3 m
B.
>1.3 m
C.
<1.3 m
D.
>2 m
Q714
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 11
A block is released from height $h(\neq0)$ on a rough track AB as shown in figure. The coefficient of friction between the block and the surface is $\mu=0.5$ and the track BC is smooth. From C onwards there is a circular smooth track of radius R=50 cm. Given $\tan\theta=\frac{3}{4}$ and $g=10~ms^{-2}$ . Based on above information, answer the following questions.
For what value of $h$ block does not leave contact with any surface.
For what value of $h$ block does not leave contact with any surface.
A.
$h = 2.5 \, \text{m}$
B.
$h \leq 2 \, \text{m}$
C.
$h = 2 \, \text{m}$
D.
$h \leq 1.5 \, \text{m}$
Q715
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 11
A block is released from height $h(\neq0)$ on a rough track AB as shown in figure. The coefficient of friction between the block and the surface is $\mu=0.5$ and the track BC is smooth. From C onwards there is a circular smooth track of radius R=50 cm. Given $\tan\theta=\frac{3}{4}$ and $g=10~ms^{-2}$ . Based on above information, answer the following questions.
If the block is placed on the above calculated height, how many times will the block cross point $C$ ?
If the block is placed on the above calculated height, how many times will the block cross point $C$ ?
A.
Infinite number of times
B.
2 times
C.
4 times
D.
3 times
Q716
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 12
A projectile of mass m=1 kg is projected with velocity $v_{0}$ at angle $\theta$ . If $\vec{a}$ be the acceleration of the projectile $\vec{v}$ be its velocity, h be its height, K be its kinetic energy and U be its potential energy at any instant, then based on above information, answer the following questions.
The magnitude of rate of change of potential energy of the projectile is numerically equal to the magnitude of
A.
$\vec{a} \times \vec{v}$
B.
$\vec{a} \cdot \vec{v}$
C.
$|\vec{a} |\times |\vec{v} |$
D.
$\frac{|\vec{a}|}{|\vec{v}|}$
Q717
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 12
A projectile of mass m=1 kg is projected with velocity $v_{0}$ at angle $\theta$ . If $\vec{a}$ be the acceleration of the projectile $\vec{v}$ be its velocity, h be its height, K be its kinetic energy and U be its potential energy at any instant, then based on above information, answer the following questions.
A graph is plotted between $\frac{K}{U}$ (on $y$ -axis), and $\frac{1}{h}$ (on $x$ -axis) then the graph will be
A.
a straight line passing through origin
B.
a straight line not passing through origin
C.
a parabola passing through origin
D.
a parabola not passing through origin
Q718
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 13
A particle of mass 2 kg moving along x axis is being acted upon by a single conservative force denoted by $F(x)$ . The potential energy of the particle is $U(x)=20+(x-2)^{2}$ , where U is in joule and x is in metre. The velocity that the particle possesses at x=5 m is $4\ ms^{-1}$ . Based on the above facts, answer the following questions.
The system possesses a mechanical energy equal to
A.
25 J
B.
35 J
C.
45 J
D.
55 J
Q719
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 13
A particle of mass 2 kg moving along x axis is being acted upon by a single conservative force denoted by $F(x)$ . The potential energy of the particle is $U(x)=20+(x-2)^{2}$ , where U is in joule and x is in metre. The velocity that the particle possesses at x=5 m is $4\ ms^{-1}$ . Based on the above facts, answer the following questions.
The maximum kinetic energy possessed by the particle is
A.
15 J
B.
25 J
C.
30 J
D.
35 J
Q720
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 13
A particle of mass 2 kg moving along x axis is being acted upon by a single conservative force denoted by $F(x)$ . The potential energy of the particle is $U(x)=20+(x-2)^{2}$ , where U is in joule and x is in metre. The velocity that the particle possesses at x=5 m is $4\ ms^{-1}$ . Based on the above facts, answer the following questions.
For what value of $x$ (say $x_0$ ) will the particle be in equilibrium?
A.
$x_0 = 1 \, \text{m}$
B.
$x_0 = 2 \, \text{m}$
C.
$x_0 = 3 \, \text{m}$
D.
$x_0 = 4 \, \text{m}$
Q721
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 14
A block of mass $m = 2 \, kg$ is suspended by a spring of force constant $k = 10 \, Nm^{-1}$ . An another spring of same value of force constant is 1 m below it. Initially both the springs were unstretched. The block is released from rest.
Based on above information, answer the following questions.
The maximum extension in the upper spring is
Based on above information, answer the following questions.
The maximum extension in the upper spring is
A.
$3.26\mathrm{m}$
B.
$1.67\mathrm{m}$
C.
$2.82\mathrm{m}$
D.
None of these
Q722
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 14
A block of mass $m = 2 \, kg$ is suspended by a spring of force constant $k = 10 \, Nm^{-1}$ . An another spring of same value of force constant is 1 m below it. Initially both the springs were unstretched. The block is released from rest.
Based on above information, answer the following questions.
The equilibrium position of the block from where it was released is
Based on above information, answer the following questions.
The equilibrium position of the block from where it was released is
A.
1 m
B.
2 m
C.
1.2 m
D.
1.5 m
Q723
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 15
The velocity versus displacement of a particle of mass 2 kg moving in a straight line is given by
$$
v = \sqrt {9 + 4 s}
$$
where v is in $ms^{-1}$ and s in metre. Based on above information, answer the following questions.
Work done by all the forces acting on the particle in a time interval from t=0 to t=2 s is
A.
10 J
B.
20 J
C.
30 J
D.
40 J
Q724
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 15
The velocity versus displacement of a particle of mass 2 kg moving in a straight line is given by
$$
v = \sqrt {9 + 4 s}
$$
where v is in $ms^{-1}$ and s in metre. Based on above information, answer the following questions.
The average power is $\frac{3}{4}^{th}$ the instantaneous power at time $t_{0}$ , then
A.
$t_{0}=1.5\ s$
B.
$t_{0}=2\ s$
C.
$t_{0}=2.5\ s$
D.
$t_{0}=3\ s$
Q725
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 16
A pendulum of mass m, length l has angular amplitude $\theta$ . Tension in the string at extreme position is $T_{1}$ and at bottom is $T_{2}$ . Based on above information, answer the following questions.
If $T_{2} = T_{1}$ , then $\theta$ is equal to
A.
$\cos^{-1}\left(\frac{1}{2}\right)$
B.
$\cos^{-1}\left(\frac{1}{3}\right)$
C.
$\cos^{-1}\left(\frac{2}{3}\right)$
D.
$\cos^{-1}\left(\frac{3}{4}\right)$
