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NLM

200 Questions Start Allen Test
All Exams Allen Advance Errorless
Q51 Allen 1. Newtons Laws of Motion MCQ
A sphere of mass 'm' is kept in equilibrium with the help of several springs as shown in the figure. Measurements show that one of the springs applies a force $\vec{F}$ on the sphere. With what acceleration the sphere will move immediately after this particular spring is cut?
A.
Zero
B.
$\frac{\vec{F}}{m}$
C.
$-\frac{\vec{F}}{m}$
D.
Insufficient information
Q52 Allen 1. Newtons Laws of Motion MCQ
Two blocks A and B of equal mass 2 kg are arranged as shown with springs $S_{1}$ and $S_{2}$ . Spring $S_{2}$ is pulled with force F = 6 N. Acceleration of block B is 4 m/s $^{2}$ towards right at an instant. If F is suddenly removed at this instant, the instantaneous acceleration of A and B will be (Assume no friction)
A.
$a_{A} = 1 \, m/s^{2}$ towards right and $a_{B} = 4 \, m/s^{2}$ left
B.
$a_{A} = 1 \, m/s^{2}$ towards left and $a_{B} = 4 \, m/s^{2}$ right
C.
$a_{A} = 1m / s^{2}$ towards left and $a_{B} = 1m / s^{2}$ right
D.
$a_{A}=0$ and $a_{B}=4\ m/s^{2}$ right
Q53 Allen 1. Newtons Laws of Motion MCQ
Statement-1: A reference frame attached to the earth is an inertial frame of reference. and Statement-2: In practical, Newton's laws can be applied in this frame of reference.
A.
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
B.
Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1.
C.
Statement-1 is True, Statement-2 is False.
D.
Statement-1 is False, Statement-2 is True.
Q54 Allen 1. Newtons Laws of Motion MCQ
A lift is going up. The total mass of the lift and the passengers is 500 kg. The speed of lift varies with time as shown in figure. What will be the tension (in kN) in the rope pulling the lift at t = 27s. $g = 9.8 \, m/s^{2}$
A.
2
B.
4
C.
6
D.
8
Q55 Allen 1. Newtons Laws of Motion MCQ
An airplane is moving horizontally with constant acceleration $5 \, m/s^{2}$ with a block of mass $2kg$ is hanging with it, which is at rest w.r.t. plane find angle $\theta$ which string makes with vertical?
A.
$\tan \theta = 2$
B.
$\cot \theta = 2$
C.
$\sin \theta = \frac {1}{2}$
D.
$\cos \theta = \frac{1}{2}$
Q56 Allen 1. Newtons Laws of Motion MCQ
If acceleration (in $m/s^{2}$ ) of wedge (rightwards) so that block does not move w.r.t. wedge is $\frac{8n}{3}$ . Value of n.
A.
7
B.
8
C.
5
D.
9
Q57 Allen 1. Newtons Laws of Motion MCQ
In the figure shown, blocks A and B move with velocities $v_{1}$ and $v_{2}$ along horizontal direction. Find the ratio of $\frac{v_{1}}{v_{2}}$ .
A.
$\frac{\cos\theta_1}{\cos\theta_2}$
B.
$\frac{\cos\theta_2}{\cos\theta_1}$
C.
$\frac{\sin\theta_2}{\sin\theta_1}$
D.
$\frac{\sin\theta_1}{\sin\theta_2}$
Q58 Allen 2. Friction MCQ
A block is moving along y-axis with velocity 4 m/s on a plank relative to ground and the plank is moving along x-axis with velocity 3 m/s at any instant of time. The unit vector in direction of friction force acting on block at this moment of time is.
A.
$\frac{3\hat{i}+4\hat{j}}{5}$
B.
$\frac{3\hat{i}-4\hat{j}}{5}$
C.
$\frac{-3\hat{i}+4\hat{j}}{5}$
D.
$\frac{-3\hat{i}-4\hat{j}}{5}$
Q59 Allen 2. Friction MCQ
For the system of blocks and pulley shown in the figure, acceleration of block is "a" and friction force acting on 10 kg block is F then :-
A.
$F = 60\ N$ , $a = 0\ m/s^2$
B.
$F = 50\ N$ , $a = \frac{20}{7}\ m/s^2$
C.
$F = 40\ N$ , $a = 0\ m/s^2$
D.
$F = 40\ N$ , $a = \frac{20}{7}\ m/s^2$
Q60 Allen 2. Friction MCQ
A block of mass 2 kg is pressed against the vertical wall of coefficient of friction $\mu = 0.2$ . The value of friction force acting on the wall is :-
A.
$40\sqrt{3} N$ in upward direction
B.
$40\sqrt{3} N$ in downward direction
C.
$20N$ in upward direction
D.
No friction force acts on the block
Q61 Allen 2. Friction MCQ
A block of mass M placed on rough surface of coefficient of friction equal to 3. If F is the $(4/5)$ of the minimum force required to just move, find out the force exerted by ground on the block.
A.
2.6 Mg
B.
Mg
C.
4Mg
D.
3.4 Mg
Q62 Allen 2. Friction MCQ
The coefficient of friction between the block and the horizontal surface is $\mu$ as shown in figure. The block moves towards right under action of horizontal force F (figure-a). Sometime later another force P is applied to the block making an angle $\theta$ (such that $\tan \theta = \mu$ ) with vertical as shown in (figure - b). After application of force P, the acceleration of block shall Fig. (a) Fig. (b)
A.
increase
B.
decrease
C.
remains same
D.
information insufficient for drawing inference.
Q63 Allen 2. Friction MCQ
A block of mass 2kg is at rest on a rough surface, of coefficient of friction 0.5. A force F is applied on the block, variation of force is represented in the figure. Speed of the block at t = 4 sec is:
A.
$2 0 m / s$
B.
$1 0 m / s$
C.
$5 m / s$
D.
$1 5 m / s$
Q64 Allen 2. Friction MCQ
Figure shows a block kept on a rough inclined plane. The maximum external force down the incline for which the block remains at rest is 2N while the maximum external force up the incline for which the block is at rest is 10 N. The coefficient of static friction $\mu$ is
A.
$\frac{\sqrt{3}}{2}$
B.
$\frac{1}{\sqrt{6}}$
C.
$\sqrt{3}$
D.
$\frac{1}{\sqrt{3}}$
Q65 Allen 2. Friction MCQ
Block A is placed on a rough wedge B which is placed on a smooth surface. The wedge has angle of inclination of $53^{\circ}$ and is imparted a horizontal acceleration g towards right. Block A is given an initial velocity $v_{0}$ with respect to wedge. Find the coefficient of friction for which block A moves with constant velocity $v_{0}$ with respect to wedge. ( $g = 10 \, m/s^{2}$ )
A.
$2 / 3$
B.
$3 / 7$
C.
$1 / 7$
D.
$1 / 3$
Q66 Allen 2. Friction MCQ
A block of mass m is at rest with respect to a rough incline kept in elevator moving up with acceleration a. Which of following statements is /are correct.
A.
The contact force between block and incline is vertical.
B.
The contact force between block and incline is of magnitude $m(g - a)$ .
C.
The contact force between block and incline is perpendicular to the incline.
D.
The contact force is of magnitude mg cos Īø.
Q67 Allen 2. Friction MCQ
A block rests on an inclined plane at an angle $\theta$ with horizontal and there is friction between the block and the plane. The plane is accelerated to the right. If the block remains at the same position on the plane, which of the following pictures might show the free-body diagram for the block? All observation is drawn for inertial observer (All of the vectors shown are forces).
A.
B.
C.
D.
Q68 Allen 2. Friction MCQ
Base angles of triangular wedge ABC are $37^{\circ}$ and $90^{\circ}$ . A uniform rope is kept over the wedge as shown in two figures. The maximum length of string which can be hanged vertically is $x_{1}$ (fig. I) and minimum length is $x_{2}$ (fig. II) in equilibrium. If $\frac{x_{1}}{x_{2}} = 3$ , find the value of coefficient of friction between rope and wedge. Fig(i) Fig(ii)
A.
0.5
B.
0.4
C.
0.6
D.
0.8
Q69 Allen 2. Friction MCQ
In the figure shown a ring of mass M and a block of mass m are in equilibrium. The string is light and pulley P does not offer any friction and coefficient of friction between pole and M is $\mu$ . The frictional force offered by the pole on M is
A.
Mg directed up
B.
$\mu mg$ directed up
C.
$(M-m)g$ directed down
D.
$\mu mg$ directed down
Q70 Allen 2. Friction MCQ
In the figure shown if friction coefficient of block 1kg and 2kg with inclined plane is $\mu_{1} = 0.5$ and $\mu_{2} = 0.4$ respectively, then
A.
both blocks will move together.
B.
both blocks will move separately.
C.
there is a non-zero contact force between two blocks.
D.
none of these
Q71 Allen 2. Friction MCQ
For shown situation the acceleration of block is represented by : (Here t is time in second) $(g = 10 \, ms^{-2})$ So, acceleration of block remains same.
A.
B.
C.
D.
None of these
Q72 Allen 2. Friction MCQ
In the figure shown, the friction coefficient between the block of mass 1 kg and the plank of mass 2 kg is 0.4 while that between the plank and floor is 0.1. A constant force ā€˜Fā€™ starts acting horizontally on the upper 1 kg block. The acceleration of plank if F = 10 N is
A.
$2.5m / s^{2}$
B.
3.833 m/s $^{4}$
C.
0.5 m/s $^{4}$
D.
$1.0m / s^{2}$
Q73 Allen 2. Friction MCQ
Three blocks of equal mass M are initially at rest on smooth floor. A force is applied to the system so that the three blocks are to move together. Mark the correct option.
A.
The minimum coefficient of friction required is $\frac{F}{3Mg}$ .
B.
The minimum coefficient of friction required is $\frac{F}{Mg}$ .
C.
The minimum coefficient of friction required is $\frac{F}{2Mg}$ .
D.
The minimum coefficient of friction required is $\frac{3F}{2Mg}$ .
Q74 Allen 3. MULTIPLE CORRECT TYPE QUESTIONS MSQ
Consider a block suspended from a light string as shown in the figure. Which of the following pairs of forces constitute Newton's third law pair?
A.
Force with which string pulls on the ceiling and the force with which string pulls on block.
B.
Force with which string pulls on the block and weight of the block.
C.
Force acting on block due to the earth and force the block exerts on the earth.
D.
Force with which block pulls on string and force with which the string pulls on the block.
Q75 Allen 3. MULTIPLE CORRECT TYPE QUESTIONS MSQ
A horse is pulling a cart on a rough surface. If take (horse + cart) as a system, then which of the following statement(s) is/are correct?
A.
Force by horse on cart is an internal force.
B.
Force by ground on horse is an external force.
C.
Force by cart on horse is an internal force.
D.
Force by ground on cart is an external force.