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Work Power and Energy

505 Questions Start Allen Test
All Exams Allen Objective Errorless
Q351 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
5 J of work is required to stretch a spring through 5 cm beyond its unstretched length. The extra work required to stretch it through additional 5 cm shall be
A.
5 J
B.
10 J
C.
15 J
D.
25 J
Q352 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
A body is dropped from a height h. When loss in its potential energy is U then its velocity is v. The mass of the body is -
A.
$\frac{U^{2}}{2v}$
B.
$\frac{2v}{U}$
C.
$\frac{2v}{U^{2}}$
D.
$\frac{2U}{v^{2}}$
Q353 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
A block of mass 4 kg is moving on a frictionless horizontal surface with velocity 2m/s and comes to rest after pressing a spring. If the force constant of the spring is 100 N/m then the compression in the spring will be -
A.
0Ā·8 m
B.
1Ā·6 m
C.
0Ā·4 m
D.
3Ā·2 m
Q354 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
A system of smooth inclined plane and block is shown in figure block is released when the spring in its natural length. Maximum elongation in the spring will be :-
A.
$\frac{2\mathrm{mg}\sin\theta}{\mathrm{K}}$
B.
$\frac{\mathrm{mg}\sin\theta}{\mathrm{K}}$
C.
$\frac{4\mathrm{mg}\sin\theta}{\mathrm{K}}$
D.
$\frac{\mathrm{mg}\sin\theta}{2\mathrm{K}}$
Q355 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
A ball of mass 2 kg is released from the tower of Pisa. The kinetic energy generated in it after falling through 10m will be ā€“
A.
20 J
B.
196 J
C.
49 J
D.
98 J
Q356 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
A stone is projected vertically up to reach maximum height 'h'. The ratio of its kinetic energy to potential energy, at a height $\frac{h}{5}$ will be:-
A.
$5:4$
B.
$4:5$
C.
$1:4$
D.
$4:1$
Q357 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
Track OABCD (as shown is figure) is smooth and fixed in vertical plane. What minimum speed has to be given to a particle lying at point A, so that it can reach point C?
A.
$60\mathrm{m / s}$
B.
$100\mathrm{m / s}$
C.
$70\mathrm{m / s}$
D.
$80\mathrm{m / s}$
Q358 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
A projectile is fired at $30^{\circ}$ with momentum p, neglecting friction, the change in kinetic energy, when it returns back to the ground, will be :-
A.
zero
B.
$30\%$
C.
$60\%$
D.
$100\%$
Q359 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
A uniform chain (mass M, length L) is released from rest from a smooth horizontal surface as shown in the figure. Velocity of the chain at the instant it completely comes out of the table will be.
A.
$V = \sqrt{gL}$
B.
$V = \sqrt{\frac{3gL}{4}}$
C.
$V = \frac{1}{2}\sqrt{5gL}$
D.
$V = \frac{1}{2}\sqrt{gL}$
Q360 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
Figure shows a plot of the potential energy as a function of x for a particle moving along the x-axis:- Which of the following statement(s) is/are true?
A.
a, c, and d are points of equilibrium
B.
a is a point of stable equilibrium
C.
b is a unstable equilibrium point
D.
All of the above
Q361 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
The graph between potential energy U and displacement X in the state of stable equilibrium will be -
A.
B.
C.
D.
Q362 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
A particle moves in a potential region given by $U = 2x^{2} - 2x + 100 \, J$ . Its state of equilibrium will be at:-
A.
x = 25 m
B.
x = 0Ā·25 m
C.
x = 0Ā·05 m
D.
x = 0Ā·5 m
Q363 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
If $F = 2x^{2} - 3x - 2$ , then choose correct option
A.
$x = -\frac{1}{2}$ is position of stable equilibrium
B.
x = 2 is position of stable equilibrium
C.
$x = -\frac{1}{2}$ is position of unstable equilibrium
D.
x = 2 is position of neutral equilibrium
Q364 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
If the potential energy of system of two molecules is given by, $U = \frac{A}{r^{12}} - \frac{B}{r^{6}}$ then at equilibrium position, its potential energy is equal to:
A.
$\frac{A^{2}}{4B}$
B.
$-\frac{B^{2}}{4A}$
C.
$\frac{2B}{A}$
D.
3A
Q365 Allen CONSERVATIVE FORCE & POTENTIAL ENERGY MCQ
A particle in a certain conservative force field has a potential energy given by $U = \frac{2x^{2}y}{z^{2}}$ . The force exerted on it is
A.
$\left(\frac{4xy}{z^{2}}\right)\hat{i}+\left(\frac{2x^{2}}{z^{2}}\right)\hat{j}+\left(\frac{4x^{2}y}{z^{3}}\right)\hat{k}$
B.
$-\left(\frac{4xy}{z^{2}}\right)\hat{i}-\left(\frac{2x^{2}}{z^{2}}\right)\hat{j}+\left(\frac{4x^{2}y}{z^{3}}\right)\hat{k}$
C.
$-\left(\frac{4xy}{z^{2}}\right)\hat{i}-\left(\frac{2x^{2}}{z^{2}}\right)\hat{j}-\left(\frac{4x^{2}y}{z^{3}}\right)\hat{k}$
D.
$\left(\frac{4xy}{z}\right)\hat{i}+\left(\frac{2x^{2}}{z}\right)\hat{j}-\left(\frac{4x^{2}y}{z^{2}}\right)\hat{k}$
Q366 Allen POWER MCQ
An electric motor produces a tension of 5000N in a load lifting cable and rolls it at the rate of 2 m/s. The power of the motor is ā€“
A.
10 kW
B.
15 kW
C.
25 kW
D.
$9 \times 10^{3}$ hp
Q367 Allen POWER MCQ
A motor of 50 hp is moving a car with a constant velocity of 36 km/hour. The forward force exerted by the engine on the car is - (1 hp = 746 W)
A.
$3 \cdot 73 \times 10^{3}$ N
B.
$3 \cdot 73 \times 10^{2}$ N
C.
$3 \cdot 73 \times 10^{1}$ N
D.
None of the above
Q368 Allen POWER MCQ
A car is moving with a speed of 36 Km/hr. If the car engine generates 7 kilowatt power, then the resistance in the path of motion of the car will be -
A.
300 newton
B.
700 newton
C.
Zero
D.
500 newton
Q369 Allen POWER MCQ
A constant force $\vec{F}$ is acting on a body of mass m moving with constant velocity $\vec{v}$ as shown in the figure. The power P exerted is
A.
Fv cosĪø
B.
$\frac{F\cos\theta}{mg}$
C.
$\frac{Fmg\cos\theta}{v}$
D.
$\frac{mg\sin\theta}{F}$
Q370 Allen POWER MCQ
A force $\vec{\mathrm{F}} = (3\hat{\mathrm{i}} + 4\hat{\mathrm{j}})\mathrm{N}$ acts on a $2\mathrm{kg}$ movable object that moves from an initial position $\overrightarrow{\mathrm{d_i}} = (-3\hat{\mathrm{i}} - 2\hat{\mathrm{j}})\mathrm{m}$ to final position $\overrightarrow{\mathrm{d_f}} = (5\hat{\mathrm{i}} + 4\hat{\mathrm{j}})$ in 6s. The average power delivered by the force during the interval is equal to:
A.
8 watt
B.
$\frac{50}{6}$ watt
C.
15 watt
D.
$\frac{50}{3}$ watt
Q371 Allen POWER MCQ
Two men with weights in the ratio 2:3 run up a staircase in times in the ratio 5:9. The ratio of power of first to that of second is -
A.
$\frac{6}{5}$
B.
$\frac{5}{6}$
C.
$\frac{10}{27}$
D.
$\frac{18}{15}$
Q372 Allen POWER MCQ
A crane lifts 200 kg weight from earth's surface up to a height of 3m in 4 seconds. The average power generated by it will be - (g = 9.8 m/sec $^{2}$ )
A.
1470 W
B.
735 W
C.
2940 W
D.
0 W
Q373 Allen POWER MCQ
Calculate power generated by tension in the string in first 2 seconds of motion :-
A.
$250\mathrm{W}$
B.
$125\mathrm{W}$
C.
$500\mathrm{W}$
D.
$750\mathrm{W}$
Q374 Allen POWER MCQ
What average horsepower is developed by a 50kg man while climbing in 10s flight of stairs that rises 10 m vertically?
A.
0.66 hp
B.
1.26 hp
C.
1.8 hp
D.
2.1 hp
Q375 Allen POWER MCQ
A 2.0 hp motor pumps out water from a well of depth 8 m and fills a water tank of volume 1492 liters at a height of 16 m from the ground. The running time of the motor to fill the empty water tank is $(g = 10m/s^{2})$ :-
A.
50 minutes
B.
10 minutes
C.
4 minutes
D.
20 minutes