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NLM

139 Questions Start Objective Test
All Exams Allen Objective Errorless
Q76 Objective 1. Taking it together MCQ
In the figure shown, a person wants to raise a block lying on the ground to a height h. In both the cases, if time required is the same, then in which case, he has to exert more force. (Assume pulleys and strings are light) (i) (ii)
A.
i
B.
ii
C.
Same in both
D.
Cannot be determined
Q77 Objective 1. Taking it together MCQ
A body of mass 2kg travels according to the relation $x(t) = pt + qt^{2} + rt^{3}$ , where $q = 4 ms^{-2}$ , $p = 3 ms^{-1}$ and $r = 5 ms^{-3}$ . The force acting on the body at t = 2 s is
A.
136 N
B.
134 N
C.
158 N
D.
68 N
Q78 Objective 1. Taking it together MCQ
A body with mass 5 kg is acted upon by a force $F = (-3\hat{i} + 4\hat{j})$ N. If its initial velocity at t = 0 is $u = (6\hat{i} - 12\hat{j}) \, \text{ms}^{-1}$ , the time at which it will just have a velocity along the Y-axis is
A.
zero
B.
10 s
C.
2 s
D.
15 s
Q79 Objective 1. Taking it together MCQ
A 5000 kg rocket is set for vertical firing. The exhaust speed is $800 \, ms^{-1}$ . To give an initial upward acceleration of $20 \, ms^{-2}$ , the amount of gas ejected per second to supply the needed thrust will be (Take, $g = 10 \, ms^{-2}$ )
A.
$127.5 \, kgs^{-1}$
B.
$187.5 \, kgs^{-1}$
C.
$185.5 \, kgs^{-1}$
D.
$137.5 \, kgs^{-1}$
Q80 Objective 1. Taking it together MCQ
Two blocks are in contact on a frictionless table. One has mass m and the other 2m. A force F is applied on 2m as shown in the figure. Now, the same force F is applied from the right on m. In the two cases, the ratio of force of contact between the two blocks will be
A.
same
B.
1:2
C.
$2:1$
D.
$1:3$
Q81 Objective 1. Taking it together MCQ
A 4 kg block A is placed on the top of 8 kg block B which rests on a smooth table. A just slips on B when a force of 12 N is applied on A. Then, the maximum horizontal force F applied on B to make both A and B move together, is
A.
12 N
B.
24 N
C.
36 N
D.
48 N
Q82 Objective 1. Taking it together MCQ
Find the value of friction forces between the blocks A and B; and between B and ground. (Take, $g=10\ ms^{-2}$ )
A.
90 N, 5 N
B.
5 N, 90 N
C.
5 N, 75 N
D.
0 N, 80 N
Q83 Objective 1. Taking it together MCQ
A block of mass 5 kg is kept on a horizontal floor having coefficient of friction 0.09. Two mutually perpendicular horizontal forces of 3 N and 4 N act on this block. The acceleration of the block is (Take, $g = 10 \, ms^{-2}$ )
A.
zero
B.
$0.1 \, ms^{-2}$
C.
$0.2 \, ms^{-2}$
D.
$0.3 \, ms^{-2}$
Q84 Objective 1. Taking it together MCQ
Two masses A and B of 10 kg and 5 kg respectively are connected with a string passing over a frictionless pulley fixed at the corner of a table as shown in figure. The coefficient of friction of A with the table is 0.2. The minimum mass of C that may be placed on A to prevent it from moving is equal to
A.
$15\mathrm{kg}$
B.
$10\mathrm{kg}$
C.
$5\mathrm{kg}$
D.
$20\mathrm{kg}$
Q85 Objective 1. 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
Q86 Objective 1. 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.
$\frac{g}{\mu}$
Q87 Objective 1. 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.
$\tan\theta = 2$
Q88 Objective 1. 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.
$\mu = \frac{\sqrt{3}}{2}$
Q89 Objective 1. 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.
$\frac{g}{6}$
Q90 Objective 1. 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.
$w\frac{a}{g}$
Q91 Objective 1. 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.
$\sqrt{\frac{2L}{(g + a)\sin\theta}}$
Q92 Objective 1. 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.
$3 \, ms^{-1}$
Q93 Objective 1. 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
Q94 Objective 1. 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
Q95 Objective 1. 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
Q96 Objective 1. 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.
$5\mathrm{ms}^{-2}$ , $5\mathrm{ms}^{-2}$
Q97 Objective 1. 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
Q98 Objective 1. 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
Q99 Objective 1. 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
Q100 Objective 1. 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