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Work Power and Energy

505 Questions Start Allen Test
All Exams Allen Objective Errorless
Q376 Allen POWER MCQ
Water is falling on the blades of a turbine at a rate of 50 kg/s from a certain spring. If the height of the spring be 50 metres, the power transferred to the turbine will be :-
A.
100 KW
B.
25 KW
C.
5 KW
D.
250 KW
Q377 Allen POWER MCQ
If the force applied is F and the velocity gained is v, then the average power developed is :-
A.
$\frac{\mathrm{F}}{\mathrm{v}}$
B.
$\frac{\mathrm{v}}{\mathrm{F}}$
C.
$\frac{\mathrm{Fv}}{2}$
D.
$\mathrm{Fv}^2$
Q378 Allen POWER MCQ
A small body of mass 'm' is located in a horizontal plane at point 0. The body accelerates uniformly and acquires horizontal velocity u then mean power developed by the friction force during the whole time of motion, if friction coefficient is k. :-
A.
$\frac{3\mathrm{mu}}{4\mathrm{kg}}$
B.
$\frac{5}{6}\mathrm{mukg}$
C.
$\frac{1}{2}\mathrm{mukg}$
D.
$\frac{12}{7}\mathrm{mukg}$
Q379 Allen POWER MCQ
A time varying power P = 2t is applied on a particle of mass 3kg. The change in kinetic energy of the particle at t = 4 sec is :-
A.
4 J
B.
8 J
C.
16 J
D.
24 J
Q380 Allen POWER MCQ
Power supplied to a particle of mass 2 kg varies with time as $P = \frac{3t^{2}}{2}$ watt. Here t is in second. If velocity of particle at t = 0 is v = 0, the velocity of particle at time t = 2 s will be :-
A.
1 m/s
B.
4 m/s
C.
2 m/s
D.
$2\sqrt{2}$ m/s
Q381 Allen POWER MCQ
A body of mass m starting from rest from origin moves along x-axis with constant power P. Calculate relation between velocity and distance :-
A.
$\mathrm{x} \propto \mathrm{v}^{1/2}$
B.
$\mathrm{x} \propto \mathrm{v}^2$
C.
$\mathrm{x} \propto \mathrm{v}$
D.
$\mathrm{x} \propto \mathrm{v}^3$
Q382 Allen POWER MCQ
A body of mass 2 kg is moving up an inclined plane rising 1 in 30 with velocity 60 m/sec. If efficiency is 40%, then calculate power required.
A.
60 W
B.
40 W
C.
100 W
D.
20 W
Q383 Allen POWER MCQ
A pump is used to deliver water at a certain rate from a given pipe. To obtain n times water from the same pipe in the same time, by what factor, the force of the motor should be increased?
A.
n times
B.
$n^{2}$ times
C.
$n^{3}$ times
D.
$\frac{1}{n}$ times
Q384 Allen PYQ MCQ
A block of mass 10 kg, moving in x direction with a constant speed of 10 m/s, is subjected to a retarding force F = 0.1x J/m during its travel from x = 20 m to 30 m. Its final KE will be :
A.
450 J
B.
275 J
C.
250 J
D.
475 J
Q385 Allen PYQ MCQ
A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is:
A.
$\sqrt{\mathrm{mk}}\mathrm{t}^{-\frac{1}{2}}$
B.
$\sqrt{2\mathrm{mk}}\mathrm{t}^{-\frac{1}{2}}$
C.
$\frac{1}{2}\sqrt{\mathrm{mk}}\mathrm{t}^{-\frac{1}{2}}$
D.
$\sqrt{\frac{\mathrm{mk}}{2}}\mathrm{t}^{-\frac{1}{2}}$
Q386 Allen PYQ MCQ
A body of mass 1 kg begins to move under the action of a time dependent force $\vec{\mathrm{F}} = (2\mathrm{t}\hat{\mathrm{i}} +3\mathrm{t}^{2}\hat{\mathrm{j}})\mathrm{N}$ , where $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ are unit vectors along x and y axis. What power will be developed by the force at the time t?
A.
$(2\mathrm{t}^2 +3\mathrm{t}^3)\mathrm{W}$
B.
$(2\mathrm{t}^2 +4\mathrm{t}^4)\mathrm{W}$
C.
$(2\mathrm{t}^3 +3\mathrm{t}^4)\mathrm{W}$
D.
$(2\mathrm{t}^3 +3\mathrm{t}^5)\mathrm{W}$
Q387 Allen PYQ MCQ
A particle moves from a point $(-2\hat{i}+5\hat{j})$ to $(4\hat{j}+3\hat{k})$ when a force of $(4\hat{i}+3\hat{j})$ N is applied. How much work has been done by the force?
A.
5 J
B.
2 J
C.
8 J
D.
11 J
Q388 Allen PYQ MCQ
Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take 'g' constant with a value $10 \, m/s^{2}$ . The work done by the (i) gravitational force and the (ii) resistive force of air is :-
A.
(i) 1.25 J (ii) - 8.25 J
B.
(i) 100 J (ii) 8.75 J
C.
(i) 10 J (ii) - 8.75 J
D.
(i) - 10 J (ii) - 8.25 J
Q389 Allen PYQ MCQ
A force $F = 20 + 10y$ acts on a particle in y-direction where $F$ is in newton and $y$ in meter. Work done by this force to move the particle from $y = 0$ to $y = 1 \, \text{m}$ is:
A.
30 J
B.
5 J
C.
25 J
D.
20 J
Q390 Allen PYQ MCQ
An object of mass 500g, initially at rest is acted upon by a variable force, whose X component varies with x in the manner shown. The velocities of the object at point X = 8 m and X = 12 m, would be the respective values of (nearly)
A.
18 m/s and 24.4 m/s
B.
23 m/s and 24.4 m/s
C.
23 m/s and 20.6 m/s
D.
18 m/s and 20.6 m/s
Q391 Allen PYQ MCQ
A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively:
A.
$\frac{S}{4}, \frac{3gS}{2}$
B.
$\frac{S}{4}, \frac{\sqrt{3gS}}{2}$
C.
$\frac{S}{2}, \frac{\sqrt{3gS}}{2}$
D.
$\frac{S}{4}, \sqrt{\frac{3gS}{2}}$
Q392 Allen PYQ MCQ
Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? (g = 10 m/s $^{2}$ )
A.
10.2 kW
B.
8.1 kW
C.
12.3 kW
D.
7.0 kW
Q393 Allen PYQ MCQ
A gravitational field is present in a region and a mass is shifted from A to B through different paths as shown. If $W_{1}$ , $W_{2}$ and $W_{3}$ represent the work done by the gravitational force along the respective paths, then :
A.
$W_{1} = W_{2} = W_{3}$
B.
$W_{1} > W_{2} > W_{3}$
C.
$W_{1} > W_{3} > W_{2}$
D.
$W_{1} < W_{2} < W_{3}$
Q394 Allen PYQ MCQ
The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm, potential energy stored in it will be:
A.
4U
B.
8U
C.
16U
D.
2U
Q395 Allen PYQ MCQ
A particle moves with a velocity $\left(5\hat{i}-3\hat{j}+6\hat{k}\right)$ m s $^{-1}$ horizontally under the action of constant force $\left(10\hat{i}+10\hat{j}+20\hat{k}\right)$ N. The instantaneous power supplied to the particle is:
A.
200 W
B.
Zero
C.
100 W
D.
140 W
Q396 Allen PYQ MCQ
At any instant of time t, the displacement of any particle is given by 2t -1 (SI unit) under the influence of force of 5N. The value of instantaneous power is (in SI unit):
A.
10
B.
5
C.
7
D.
6
Q397 Allen PYQ MCQ
An object moving along horizontal x-direction with kinetic energy 10 J is displaced through $x = \left(3\hat{i}\right)$ m by the force $\vec{F} = \left(-2\hat{i} + 3\hat{j}\right)N$ . The kinetic energy of the object at the end of the displacement x is:
A.
10 J
B.
16 J
C.
4 J
D.
6 J
Q398 Allen PYQ MCQ
An object falls from a height of 10 m above the ground. After striking the ground it loses 50% of its kinetic energy. The height upto which the object can rebound from the ground is:
A.
7.5 m
B.
10 m
C.
2.5 m
D.
5 m
Q399 Allen (Analytical Questions) MCQ
Select the correct statements -
(a) Work done by conservative force along closed path is zero.
(b) A body with negative energy can't have linear momentum
(c) Net work done by all the internal force of a system is independent of choice of reference frame
(d) Work done by a non conservative force is always negative
A.
a, b and c
B.
a and c
C.
a, b and d
D.
All
Q400 Allen (Analytical Questions) MCQ
Select the correct statements - (a) Potential energy is defined only for gravitational force. (b) Potential energy can be associated with frictional force. (c) Work done by spring force is equal to change in potential energy of the spring.
A.
a and b
B.
a and c
C.
all
D.
none of these