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90 Questions MSQ (Multiple Correct) Start Allen Test
All Exams Allen Advance Errorless
JEE (Advanced) 2021 Q1 Errorless JEE Section MSQ
One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight $\alpha W$ is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of $(2\sqrt{2})W$ . Which of the following statement(s) is(are) correct
A.
The vertical component of reaction force at O does not depend on $\alpha$
B.
The horizontal component of reaction force at O is equal to W for $\alpha = 0.5$
C.
The tension in the rope is 2W for $\alpha = 0.5$
D.
The rope breaks if $\alpha > 1.5$
JEE (Advanced) 2014 Q2 Advance ARCHIVE: JEE ADVANCED MSQ
In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle $\theta$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $\mu_{1}$ and that between the floor and the ladder is $\mu_{2}$ . The normal reaction of the wall on the ladder is $N_{1}$ and that of the floor is $N_{2}$ . If the ladder is about to slip, then
A.
$\mu_{1} = 0, \mu_{2} \neq 0$ and $N_{2}\tan \theta = \frac{mg}{2}$
B.
$\mu_{1} \neq 0$ , $\mu_{2} = 0$ and $N_{1} \tan \theta = \frac{mg}{2}$
C.
$\mu_{1} \neq 0, \mu_{2} \neq 0$ and $N_{2} = \frac{mg}{1 + \mu_{1}\mu_{2}}$
D.
$\mu_{1} = 0, \mu_{2} \neq 0$ and $N_{1}\tan \theta = \frac{mg}{2}$
WB-JEE 2013 Q3 Errorless JEE Section MSQ
A block of mass $m(=0.1kg)$ is hanging over a frictionless light fixed pulley by an inextensible string of negligible mass. The other end of the string is pulled by a constant force F in the vertically downward direction. The linear momentum of the block increase by $2kg\,ms^{-1}$ in 1 s after the block starts from rest. Then, (given $g=10\,ms^{-2}$ )
A.
The tension in the string is $F$
B.
The tension in the string is $3N$
C.
The work done by the tension on the block is $20J$ during this 1 s
D.
The work done against the force of gravity is 10 J
IIT JEE 2012 Q4 Errorless More than One Correct Answers MSQ
A small block of mass of 0.1kg lies on a fixed inclined plane PQ which makes an angle $\theta$ with the horizontal. A horizontal force of 1N acts on the block through its center of mass as shown in the figure. The block remains stationary if (take g = 10m/s $^{2}$ )
A.
$\theta = 45^{\circ}$
B.
$\theta > 45^{\circ}$ and a frictional force acts on the block towards P
C.
$\theta > 45^{\circ}$ and a frictional force acts on the block towards $Q$
D.
$\theta < 45^{\circ}$ and a frictional force acts on the block towards $Q$
IIT-JEE 2012 Q5 Advance ARCHIVE: JEE ADVANCED MSQ
A small block of mass of 0.1 kg lies on a fixed inclined plane PQ which makes an angle $\theta$ with the horizontal. A horizontal force of 1 N acts on the block through its centre of mass as shown in the figure. The block remains stationary if (take $g = 10 \, ms^{-2}$ )
A.
$\theta = 45^{\circ}$ .
B.
$\theta > 45^{\circ}$ and a frictional force acts on the block towards P.
C.
$\theta > 45^{\circ}$ and a frictional force acts on the block towards Q.
D.
$\theta < 45^{\circ}$ and a frictional force acts on the block towards $Q$ .
2000 Q6 Advance MULTIPLE CORRECT CHOICE TYPE QUESTIONS MSQ
An engine of mass $5 \times 10^{4}$ kg pulls a coach of mass $4 \times 10^{4}$ kg. A resistance of 1 N per 100 kg is acting on both the coach and the engine and if the driving force of the engine is 4500 N then
A.
the acceleration of the system (coach + engine) is $0.04 \, ms^{-2}$ .
B.
the acceleration of the system (coach + engine) is $0.05 \, ms^{-2}$ .
C.
the tension in the coupling is 2000 N.
D.
the tension in the coupling is 2400 N.
IIT-JEE 1986 Q7 Advance ARCHIVE: JEE ADVANCED MSQ
A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limits $-\phi$ and $+\phi$ . For an angular displacement $\theta(|\theta|<\phi)$ , the tension in the string and the velocity of the bob are T and V respectively. The following relations hold good under the above conditions
A.
$T \cos \theta = Mg$
B.
$T - Mg \cos \theta = \frac{MV^{2}}{L}$
C.
The magnitude of the tangential acceleration of the bob $\left|a_{T}\right|=g\sin\theta.$
D.
$T = Mg \cos \theta$
IIT-JEE 1986 Q8 Advance ARCHIVE: JEE ADVANCED MSQ
A reference frame attached to the earth
A.
is an inertial frame by definition.
B.
cannot be an inertial frame because of revolution of earth round the sun.
C.
is an inertial frame because Newton's laws are applicable in this frame.
D.
cannot be an inertial frame because of rotation of earth about its own axis.
Q9 Allen 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.
Q10 Allen 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.
Q11 Allen MULTIPLE CORRECT TYPE QUESTIONS MSQ
For the system shown which of the option(s) are CORRECT :
A.
$N\cos \theta = mg$
B.
$N = mg\cos \theta$
C.
N - mg cos θ = ma
D.
$mg - N \cos \theta = ma \sin \theta$
Q12 Allen MULTIPLE CORRECT TYPE QUESTIONS MSQ
A ball is attached from the ceiling with help of three equal taut strings each making equal angle with vertical and equal angle with each other. The ball is under three forces of pull due to the string which are along the length of strings and the force of gravity acting vertically downwards.
A.
resultant of the four forces on the ball can be zero.
B.
resultant of the four forces on the ball can never be zero.
C.
If one string is cut and its force becomes zero, the ball can remain in equilibrium in that position.
D.
If one string is cut and its force becomes zero, the ball can never be in equilibrium in that position.
Q13 Allen MULTIPLE CORRECT TYPE QUESTIONS MSQ
A carpenter of mass 50 kg is standing on a weighing machine placed in a lift of mass 20 kg. A light string is attached to the lift. The string passes over a smooth pulley and the other end is held by the carpenter as shown. When carpenter keeps the lift moving upward with constant velocity: $(g = 10 \, m/s^{2})$
A.
the reading of weighing machine is 15 kg
B.
the man applies a force of 350 N on the string
C.
net force on the man is 150 N
D.
Net force on the weighing machine is 150 N
Q14 Allen MULTIPLE CORRECT TYPE QUESTIONS MSQ
In the given figure $m_{1} = 1kg$ , $m_{2} = 2kg$ , $m_{3} = 3kg$ , F = 18 N and spring constant is 100 N/m then choose the correct options. (Assume string and spring are ideal)
A.
Acceleration of $m_{1}$ is $2 \, m/s^{2}$
B.
Tension in string is 2N
C.
Force applied by spring on block of mass $m_{2}$ is 6N
D.
Acceleration of block of mass $m_{3}$ is $4 \, m/s^{2}$
Q15 Allen MULTIPLE CORRECT TYPE QUESTIONS MSQ
A sleeve S of mass m starts sliding down along a smooth inclined rod through a vertical distance h from rest. Cart(C) carrying the rod is moving with constant horizontal acceleration a. If N is the normal force between sleeve and rod, $V_{S/C}$ is the speed of sleeve relative to cart on reaching the lowest point and T is the time taken to reach lowest point then :
A.
$N = m$ $(g\cos \theta +a\sin \theta)$
B.
$V_{S/C} = \sqrt{2h(g - a\cot\theta)}$
C.
$V_{S/C} = \sqrt{2h(g - a\tan\theta)}$
D.
$T = \sqrt{\frac{2h}{\sin\theta(g\cos\theta - a\sin\theta)}}$
Q16 Allen MULTIPLE CORRECT TYPE QUESTIONS MSQ
A ball of mass m is placed on a sledge of mass M. The sledge moves on an inclined plane A of angle of inclination $\theta$ . Inclined plane A is moving with constant horizontal acceleration ‘a’ towards left (Neglect friction everywhere)
A.
Normal reaction force between m and M is $m(g \cos \theta + a \sin \theta)$
B.
Normal reaction force between A and M is $(M + m)$ ( $g \cos \theta + a \sin \theta$ )
C.
$a_{M / A} = a_{m / A} = (g\sin \theta -a\cos \theta)$
D.
$a_{M} = a_{m} = \sin \theta \sqrt{g^{2} + a^{2}}$
Q17 Allen MULTIPLE CORRECT TYPE QUESTIONS MSQ
A block of m = 10 kg is kept on ground. A vertically upward force $F = (10 \ t)N$ , where t is the time in seconds starts acting on it at t = 0 as shown in figure.
A.
Time at which block loose contact from the surface is 10 sec.
B.
Velocity of block at t = 20 sec is 50 m/s.
C.
Velocity of block at t = 20 sec is 200 m/s.
D.
Displacement of block in 20 sec is $\frac{500}{3}$ m.
Q18 Allen MULTIPLE CORRECT TYPE QUESTIONS MSQ
System shown in the figure is released from rest. Which of the following statements is/are true? $[g = 10 \, m/s^{2}]$
A.
Magnitude of acceleration of each block is $3 \, m/s^{2}$ .
B.
Tension in the cord A is 6.5 N.
C.
Tension in the cord B is 8 N.
D.
Difference of magnitudes of tensions in both the cord is 1.5 N.
Q19 Allen MULTIPLE CORRECT TYPE QUESTIONS MSQ
A block A and wedge B connected through a string as shown. The wedge B is moving away from the wall with acceleration $2 \, m/s^{2}$ horizontally and acceleration of block A is vertically upwards. Then
A.
Acceleration of A with respect to B is $4 \, m/s^{2}$ .
B.
Acceleration of A with respect to B is $2\sqrt{3}$ m/s $^{2}$ .
C.
Angle $\theta$ is $60^{\circ}$ .
D.
Acceleration of A is $2\sqrt{3}$ m/s $^{2}$ .
Q20 Allen MULTIPLE CORRECT TYPE QUESTIONS MSQ
A block is kept on a rough surface and applied with a horizontal force as shown which is gradually increasing from zero. The coefficient of static and kinetic friction are $\frac{1}{\sqrt{3}}$ then image.png
A.
When F is less than the limiting friction, angle made by net force on the block by the surface is less than $30^{\circ}$ with vertical.
B.
When the block is just about to move, the angle made by net force by the surface on the block becomes equal to $30^{\circ}$ with vertical.
C.
When the block starts to accelerate, the angle made by net force by the surface on the block becomes constant and equal to $30^{\circ}$ vertical.
D.
The angle made by net force with vertical on the block by the surface, depends on the mass of the block.
Q21 Allen MULTIPLE CORRECT TYPE QUESTIONS MSQ
A block placed on a rough horizontal surface is pushed with a force F acting horizontally on the block. The magnitude of F is increased and acceleration produced is plotted in the graph shown.
A.
Mass of the block is 2 kg.
B.
Coefficient of friction between block and surface is 0.5.
C.
Limiting friction between block and surface is 10 N.
D.
When F = 8 N, friction between block and surface is 10 N.
Q22 Allen MULTIPLE CORRECT TYPE QUESTIONS MSQ
A block placed on rough inclined plane is pushed with a force F. The coefficient of friction is $\mu = 0.5$ and mass of block is 10 kg.
A.
If F = 30 N, acceleration of block is zero and friction acting on block is 30 N.
B.
If F = 60 N, acceleration of block is zero and friction acting on block is 60 N.
C.
If $F = 90N$ , acceleration of block is zero and friction acting on block is $30N$ .
D.
If F = 120 N, acceleration of block is $2 \, m/s^{2}$ and friction acting on block is 40 N.
Q23 Allen JEE Advanced Practice Paper MSQ
Refer the system shown in the figure. Block is sliding down the wedge. All surfaces are frictionless. Find correct statement(s)
A.
Acceleration of block is $g \sin \theta$
B.
Acceleration of block is $g \cos \theta$
C.
Tension in the string is $mg \cos 2\theta$
D.
Tension in the string is mg sin θ.cos θ
Q24 Allen JEE Advanced Practice Paper MSQ
The mass in the figure can slide on a frictionless surface. When the mass is pulled out, spring 1 is stretched a distance $x_{1}$ and spring 2 is stretched a distance $x_{2}$ . The spring constants are $k_{1}$ and $k_{2}$ respectively. Total magnitude of spring force pulling back on the mass is
A.
$k _ {1} x _ {1}$
B.
$k _ {2} x _ {2}$
C.
$\left(k _ {1} x _ {1} + k _ {2} x _ {2}\right)$
D.
0.5 $(k_{1} + k_{2})(x_{1} + x_{2})$
Q25 Allen JEE Advanced Practice Paper MSQ
In the given figure both the blocks have equal mass. When the thread is cut, which of the following statements give correct description immediately after the thread is cut?
A.
Relative to the block A, acceleration of block B is 2g upwards.
B.
Relative to the block B, acceleration of block A is 2g downwards.
C.
Relative to the ground, accelerations of the blocks A and B are both g downwards.
D.
Relative to the ground, accelerations of the blocks A and B are 2g downwards and zero respectively.