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629 Questions Start Allen Test
All Exams Allen Objective Errorless
Q551 Objective Taking it together MCQ
In the figure, pulleys are smooth and strings are massless, $m_{1}=1$ kg and $m_{2}=\frac{1}{3}$ kg. To keep $m_{3}$ at rest, mass $m_{3}$ should be
A.
1 kg
B.
$\frac{2}{3}$ kg
C.
$\frac{1}{4}$ kg
D.
2 kg
Q552 Objective Taking it together MCQ
If the coefficient of friction between A and B is $\mu$ , the maximum acceleration of the wedge A for which B will remain at rest with respect to the wedge is
A.
$\mu g$
B.
$g\left(\frac{1 + \mu}{1 - \mu}\right)$
C.
$g\left(\frac{1 - \mu}{1 + \mu}\right)$
D.
$\frac{g}{\mu}$
Q553 Objective Taking it together MCQ
A block of mass 1 kg is at rest relative to a smooth wedge moving leftwards with constant acceleration $a = 5 \, ms^{-2}$ . Let N be the normal reaction between the block and the wedge. Then, (Take, $g = 10 \, ms^{-2}$ )
A.
$N = 5\sqrt{5} \, N$
B.
N = 15 N
C.
$\tan\theta = \frac{1}{3}$
D.
$\tan\theta = 2$
Q554 Objective Taking it together MCQ
A block of mass m is kept on an inclined plane of a lift moving down with acceleration of $2 \, ms^{-2}$ . What should be the coefficient of friction to let the block move down with constant velocity relative to lift?
A.
$\mu = \frac{1}{\sqrt{3}}$
B.
$\mu = 0.4$
C.
$\mu = 0.8$
D.
$\mu = \frac{\sqrt{3}}{2}$
Q555 Objective Taking it together MCQ
Two blocks of mass 5 kg and 3 kg are attached to the ends of a string passing over a smooth pulley fixed to the ceiling of an elevator. The elevator is accelerated upwards. If the acceleration of the blocks is $\frac{9}{32}g$ , the acceleration of the elevator is
A.
$\frac{g}{3}$
B.
$\frac{g}{4}$
C.
$\frac{g}{8}$
D.
$\frac{g}{6}$
Q556 Objective Taking it together MCQ
A balloon of weight w is falling vertically downward with a constant acceleration $a (< g)$ . The magnitude of the air resistance is
A.
w
B.
$w\left(1+\frac{a}{g}\right)$
C.
$w\left(1-\frac{a}{g}\right)$
D.
$w\frac{a}{g}$
Q557 Objective Taking it together MCQ
A smooth inclined plane of length L, having an inclination $\theta$ with horizontal is inside a lift which is moving down with retardation a. The time taken by a block to slide down the inclined plane from rest will be
A.
$\sqrt{\frac{2L}{\sqrt{a\sin\theta}}}$
B.
$\sqrt{\frac{2L}{g\sin\theta}}$
C.
$\sqrt{\frac{2L}{(g - a)\sin\theta}}$
D.
$\sqrt{\frac{2L}{(g + a)\sin\theta}}$
Q558 Objective Taking it together MCQ
A body of mass M at rest explodes into three pieces, two of which of mass M/4 each are thrown off in perpendicular directions with velocities of $3 \, ms^{-1}$ and $4 \, ms^{-1}$ , respectively. The third piece will be thrown off with a velocity of
A.
$1.5 \, ms^{-1}$
B.
$2 \, ms^{-1}$
C.
$2.5 \, ms^{-1}$
D.
$3 \, ms^{-1}$
Q559 Objective Taking it together MCQ
A wooden box of mass 8 kg slides down an inclined plane of inclination $30^{\circ}$ to the horizontal with a constant acceleration of $0.4 \, ms^{-2}$ . What is the force of friction between the box and inclined plane? (Take, $g = 10 \, ms^{-2}$ )
A.
36.8 N
B.
76.8 N
C.
65.6 N
D.
None of these
Q560 Objective Taking it together MCQ
A mass of 3 kg descending vertically downwards supports a mass of 2 kg by means of a light string passing over a pulley. At the end of 5 s, the string breaks . How much high from now the 2 kg mass will go? (Take, $g = 9.8 \, ms^{-2}$ )
A.
4.9 m
B.
9.8 m
C.
19.6 m
D.
2.45 m
Q561 Objective Taking it together MCQ
The rear side of a truck is open and a box of mass 20 kg is placed on the truck 4 m away from the open end ( $\mu = 0.15$ and $g = 10 \, ms^{-2}$ ). The truck starts from rest with an acceleration of $2 \, ms^{-2}$ on a straight road. The box will fall off the truck when it is at a distance from the starting point equal to
A.
4 m
B.
8 m
C.
16 m
D.
32 m
Q562 Objective Taking it together MCQ
Two blocks of masses $m = 5\mathrm{kg}$ and $M = 10\mathrm{kg}$ are connected by a string passing over a pulley $B$ as shown. Another string connects the centre of pulley $B$ to the floor and passes over another pulley $A$ as shown. An upward force $F$ is applied at the centre of pulley $A$ . Both the pulleys are massless. The accelerations of blocks $m$ and $M$ , if $F$ is $300\mathrm{N}$ are (Take, $g = 10\mathrm{ms}^{-2}$ )
A.
$5\mathrm{ms}^{-2}$ , zero
B.
zero, $5\mathrm{ms}^{-2}$ ;
C.
zero, zero
D.
$5\mathrm{ms}^{-2}$ , $5\mathrm{ms}^{-2}$
Q563 Objective Taking it together MCQ
A man of mass m stands on a platform of equal mass m and pulls himself by two ropes passing over pulleys as shown in figure. If he pulls each rope with a force equal to half his weight, his upward acceleration would be
A.
$\frac{g}{2}$
B.
$\frac{g}{4}$
C.
g
D.
zero
Q564 Objective Taking it together MCQ
A 40 N block supported by two ropes. One rope is horizontal and the other makes an angle of $30^{\circ}$ with the ceiling. The tension in the rope attached to the ceiling is approximately
A.
80 N
B.
40 N
C.
$40\sqrt{3}$ N
D.
$\frac{40}{\sqrt{3}}$ N
Q565 Objective Taking it together MCQ
Starting from rest, a body slides down a $45^{\circ}$ inclined plane in twice the time, it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is
A.
0.2
B.
0.25
C.
0.75
D.
0.5
Q566 Objective Taking it together MCQ
A block of mass 0.1 kg is held against a wall applying a horizontal force of 5 N on the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of the frictional force acting the block is
A.
2.5 N
B.
0.98 N
C.
4.9 N
D.
0.49 N
Q567 Objective Taking it together MCQ
A block of mass m is given an initial downward velocity $v_{0}$ and left on an inclined plane (coefficient of friction=0.6). The block will
A.
continue of move down the plane with constant velocity $v_{0}$
B.
accelerate downward
C.
decelerate and come to rest
D.
first accelerate downward then decelerate
Q568 Objective Taking it together MCQ
Pushing force making an angle $\theta$ to the horizontal is applied on a block of weight $w$ placed on a horizontal table. If the angle of friction is $\phi$ , the magnitude of force required to move the body is equal to
A.
$\frac{w \cos \phi}{\cos(\theta - \phi)}$
B.
$\frac{w \sin \phi}{\cos(\theta + \phi)}$
C.
$\frac{w \tan \phi}{\sin(\theta - \phi)}$
D.
$\frac{w \sin \phi}{\tan(\theta - \phi)}$
Q569 Objective Taking it together MCQ
In the arrangement shown in figure, there is a friction force between the blocks of masses m and 2m kept on a smooth horizontal surface. The mass of the suspended block is m. The block of mass m is stationary with respect to block of mass 2 m. The minimum value of coefficient of friction between m and 2 m is ____
A.
$\frac{1}{2}$
B.
$\frac{1}{\sqrt{2}}$
C.
$\frac{1}{4}$
D.
$\frac{1}{3}$
Q570 Objective Taking it together MCQ
Two masses m and M are attached with strings as shown. For the system to be in equilibrium, we have
A.
$\tan\theta=1+\frac{2M}{m}$
B.
$\tan\theta=1+\frac{2m}{M}$
C.
$\tan\theta=1+\frac{M}{2m}$
D.
$\tan\theta=1+\frac{m}{2M}$
Q571 Objective Taking it together MCQ
A man of mass m has fallen into a ditch of width d. Two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in figure. Both the friends exert force of equal magnitudes $F$ . exert force of equal magnitudes $F$ . When the man is at a depth $h$ , the value of $F$ is
A.
$\frac{mg}{4h}\sqrt{d^2 + 4h^2}$
B.
$hmg$
C.
$dmg$
D.
$\frac{mg}{2h}\sqrt{h^2 + d^2}$
Q572 Objective Taking it together MCQ
Two weights $w_{1}$ and $w_{2}$ are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up with an acceleration g. The tension in the string will be
A.
$\frac{4w_{1}w_{2}}{w_{1}+w_{2}}$
B.
$\frac{2w_{1}w_{2}}{w_{1}+w_{2}}$
C.
$\frac{w_{1}-w_{2}}{w_{1}+w_{2}}$
D.
$\frac{w_{1}w_{2}}{2(w_{1}+w_{2})}$
Q573 Objective Taking it together MCQ
A dynamometer D is attached to two bodies of masses M = 6 kg and m = 4 kg. Forces F = 20N and f = 10N are applied to the masses as shown. The dynamometer reads
A.
$10\mathrm{N}$
B.
$20\mathrm{N}$
C.
$6\mathrm{N}$
D.
$14\mathrm{N}$
Q574 Objective Taking it together MCQ
Two blocks are connected over a massless pulley as shown in figure. The mass of block A is 10 kg and the coefficient of kinetic friction is 0.2. Block A slides down the incline at constant speed. The mass of block B (in kg) is
A.
5.4
B.
3.3
C.
4.2
D.
6.8
Q575 Objective Taking it together MCQ
A block of mass 5 kg resting on a horizontal surface is connected by a cord, passing over a light frictionless pulley to a hanging block of mass 5 kg. The coefficient of kinetic friction between the block and the surface is 0.5. Tension in the cord is (Take, $g = 9.8 \, ms^{-2}$ )
A.
$49\mathrm{N}$
B.
zero
C.
$36.75\mathrm{N}$
D.
$12.75\mathrm{N}$