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NLM

629 Questions Start Allen Test
All Exams Allen Objective Errorless
Q526 Objective Taking it together MCQ
Conservation of momentum in a collision between particles can be understood from
A.
conservation of energy
B.
Newton's first law only
C.
Newton's second law only
D.
Both Newton's second and third law
Q527 Objective Taking it together MCQ
If the elevator in the shown figure is moving upwards with constant acceleration $1 \, ms^{-2}$ , the tension in the string connected to block A of mass 6 kg would be (Take, $g = 10 \, ms^{-2}$ )
A.
60 N
B.
66 N
C.
54 N
D.
42 N
Q528 Objective Taking it together MCQ
A block is placed on the top of a smooth inclined plane of inclination $\theta$ kept on the floor of a lift. When the lift is descending with a retardation a, the block is released. The acceleration of the block relative to the incline is
A.
$g \sin \theta$
B.
$a \sin \theta$
C.
$(g - a) \sin \theta$
D.
$(g + a) \sin \theta$
Q529 Objective Taking it together MCQ
A cricket ball of mass 150 g has an initial velocity $\mathbf{u} = (3\hat{\mathbf{i}} + 4\hat{\mathbf{j}}) \, \mathrm{ms}^{-1}$ and a final velocity $\mathbf{v} = -(3\hat{\mathbf{i}} + 4\hat{\mathbf{j}}) \, \mathrm{ms}^{-1}$ , after being hit. The change in momentum (final momentum ā€“ initial momentum) is (in kgĀ·ms $^{-1}$ )
A.
zero
B.
$-(0.45\hat{\mathbf{i}} + 0.6\hat{\mathbf{j}})$
C.
$-(0.9\hat{\mathbf{i}} + 1.2\hat{\mathbf{j}})$
D.
$-5(\hat{\mathbf{i}} + \hat{\mathbf{j}})\hat{\mathbf{i}}$
Q530 Objective Taking it together MCQ
In the previous question (5), the magnitude of the momentum transferred during the hit is
A.
zero
B.
$0.75 \, kg \cdot ms^{-1}$
C.
$1.5 \, kg \cdot ms^{-1}$
D.
$14 \, kg \cdot ms^{-1}$
Q531 Objective Taking it together MCQ
A block of mass m is placed on a smooth plane inclined at an angle $\theta$ with the horizontal. The force exerted by the plane on the block has a magnitude
A.
mg
B.
mg sec $\theta$
C.
mg cos $\theta$
D.
mg sin $\theta$
Q532 Objective Taking it together MCQ
A block has been placed on an inclined plane. The slope angle $\theta$ of the plane is such that the block slides down the plane at a constant speed. The coefficient of kinetic friction is equal to
A.
$\sin\theta$
B.
$\cos\theta$
C.
g
D.
$\tan\theta$
Q533 Objective Taking it together MCQ
A body is projected up a $45^{\circ}$ rough incline. If the coefficient of friction is 0.5, then the retardation of the block is
A.
$\frac{g}{2\sqrt{2}}$
B.
$\frac{g}{\sqrt{2}}$
C.
$\frac{3g}{2\sqrt{2}}$
D.
$\frac{g}{2}$
Q534 Objective Taking it together MCQ
A rope of length L and mass M is hanging from a rigid support. The tension in the rope at a distance x from the rigid support is
A.
Mg
B.
$\left(\frac{L-x}{L}\right)Mg$
C.
$\left(\frac{L}{L-x}\right)Mg$
D.
$\frac{x}{L}Mg$
Q535 Objective Taking it together MCQ
Consider the shown arrangement. Assume all surfaces to be smooth. If N represents magnitudes of normal reaction between block and wedge, then acceleration of M along horizontal is equal to
A.
$\frac{N\sin\theta}{M}$ along + ve $X$ -axis
B.
$\frac{N\cos\theta}{M}$ along -ve $X$ -axis
C.
$\frac{N\sin\theta}{M}$ along -ve $X$ -axis
D.
$\frac{N\sin\theta}{m + M}$ along -ve $X$ -axis
Q536 Objective Taking it together MCQ
In the above problem, normal reaction between ground and wedge will have magnitude equal to
A.
$N \cos \theta + Mg$
B.
$N \cos \theta + Mg + mg$
C.
$N \cos \theta - Mg$
D.
$N \sin \theta + Mg + mg$
Q537 Objective Taking it together MCQ
A block of mass m is at rest on an inclined plane which is making angle $\theta$ with the horizontal. The coefficient of friction between the block and plane is $\mu$ . Then, frictional force acting between the surfaces is
A.
$\mu mg$
B.
$\mu mg\sin \theta$
C.
$\mu (mg\sin \theta -mg\cos \theta)$
D.
$mg\sin \theta$
Q538 Objective Taking it together MCQ
If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest?
A.
1cm
B.
2 cm
C.
3 cm
D.
4 cm
Q539 Objective Taking it together MCQ
An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given by
A.
$\cot \alpha = 3$
B.
$\tan \alpha = 3$
C.
$\sec \alpha = 3$
D.
$\csc \alpha = 3$
Q540 Objective Taking it together MCQ
A hockey player is moving northward and suddenly turns westward with the same speed to avoid an opponent. The force that acts on the player is
A.
frictional force along westward
B.
muscle force along southward
C.
frictional force along south-west
D.
muscle force along south-west
Q541 Objective Taking it together MCQ
A car of mass m starts from rest and acquires a velocity along east $\mathbf{v} = v\hat{\mathbf{i}}(v > 0)$ in two seconds. Assuming the car moves with uniform acceleration, the force exerted on the car is
A.
$\frac{mv}{2}$ eastward and is exerted by the car engine
B.
$\frac{mv}{2}$ eastward and is due to the friction on the tyres exerted by the road
C.
more than $\frac{mv}{2}$ eastward exerted due to the engine and overcomes the friction of the road
D.
$\frac{mv}{2}$ exerted by the engine
Q542 Objective 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
Q543 Objective 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
Q544 Objective 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
Q545 Objective 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.
$137.5 \, kgs^{-1}$
Q546 Objective 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.
$1:3$
Q547 Objective 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
Q548 Objective 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
Q549 Objective 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.
$0.3 \, ms^{-2}$
Q550 Objective 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.
$20\mathrm{kg}$