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968 Questions Start Allen Test
All Exams Allen Advance Errorless
Q376 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
Q377 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 $4 \, m/s^{2}$
Q378 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.
$T = \sqrt{\frac{2h}{\sin\theta(g\cos\theta - a\sin\theta)}}$
Q379 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 ā€˜aā€™ 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.
$a_{M} = a_{m} = \sin \theta \sqrt{g^{2} + a^{2}}$
Q380 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.
Q381 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.
Q382 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 $^{2}$ .
Q383 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.
Q384 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.
Q385 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.
Q386 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 63 TO 66

A uniform rope of mass $(m)$ and length $(L)$ placed on frictionless horizontal ground is being pulled by two forces $F_{A}$ and $F_{B}$ at its ends as shown in the figure. As a result, the rope accelerates toward the right. Acceleration (a) of the rope is
A.
zero
B.
$a = \frac{F_{A} + F_{B}}{m}$
C.
$a = \frac{F_{A} - F_{B}}{m}$
D.
$a = \frac{F_{B} - F_{A}}{m}$
Q387 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 63 TO 66

A uniform rope of mass $(m)$ and length $(L)$ placed on frictionless horizontal ground is being pulled by two forces $F_{A}$ and $F_{B}$ at its ends as shown in the figure. As a result, the rope accelerates toward the right. Tension (T) at the mid point of the rope is
A.
$T = F_{B} - F_{A}$
B.
$T = F_{A} + F_{B}$
C.
$T = \frac{1}{2}(F_{B} - F_{A})$
D.
$T = \frac{1}{2}(F_{A} + F_{B})$
Q388 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 63 TO 66

A uniform rope of mass $(m)$ and length $(L)$ placed on frictionless horizontal ground is being pulled by two forces $F_{A}$ and $F_{B}$ at its ends as shown in the figure. As a result, the rope accelerates toward the right. Expression $(T_{x})$ of tension at a point at distance $x$ from the end $A$ is
A.
$T_{x} = \left(\frac{F_{B} - F_{A}}{L}\right)x + F_{A}$
B.
$T_{x} = \left(\frac{F_{B} - F_{A}}{L}\right)x - F_{A}$
C.
$T_{x} = \left(\frac{F_{B} - F_{A}}{L}\right)x + F_{B}$
D.
$T_{x} = \left(\frac{F_{B} - F_{A}}{L}\right)x - F_{B}$
Q389 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 63 TO 66

A uniform rope of mass $(m)$ and length $(L)$ placed on frictionless horizontal ground is being pulled by two forces $F_{A}$ and $F_{B}$ at its ends as shown in the figure. As a result, the rope accelerates toward the right. Which of the following graph best represents variation in tension at a point on the rope with distance x of the point from the end A?
A.
B.
C.
D.
Q390 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 67 TO 69

A block of mass m is placed on a smooth horizontal floor is attached to one end of spring. The other end of the spring is attached to fixed support. When spring is vertical it is relaxed. Now the block is pulled towards right by a force F, which is being increased gradually. When the spring makes angle $53^{\circ}$ with the vertical, block leaves the floor. When blocks leaves the table, the normal force on it from table is
A.
mg
B.
zero
C.
$\frac{4mg}{3}$
D.
$\frac{3mg}{4}$
Q391 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 67 TO 69

A block of mass m is placed on a smooth horizontal floor is attached to one end of spring. The other end of the spring is attached to fixed support. When spring is vertical it is relaxed. Now the block is pulled towards right by a force F, which is being increased gradually. When the spring makes angle $53^{\circ}$ with the vertical, block leaves the floor. Force constant of the spring is :-
A.
$\frac{5mg}{2\ell}$
B.
$\frac{15mg}{8\ell}$
C.
$\frac{5mg}{3\ell}$
D.
$\frac{5mg}{4\ell}$
Q392 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 67 TO 69

A block of mass m is placed on a smooth horizontal floor is attached to one end of spring. The other end of the spring is attached to fixed support. When spring is vertical it is relaxed. Now the block is pulled towards right by a force F, which is being increased gradually. When the spring makes angle $53^{\circ}$ with the vertical, block leaves the floor. When the block leaves the table, the force F is :-
A.
$\frac{3mg}{4}$
B.
$\frac{4mg}{3}$
C.
$\frac{3mg}{5}$
D.
$\frac{4mg}{5}$
Q393 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 70 TO 72

In the figure shown blocks A and B are of mass 2 kg and 8 kg and they are connected through strings to a spring connected to ground. The blocks are in equilibrium. $(g = 10m/s^{2})$ The elongation of the spring is
A.
1 cm
B.
10 cm
C.
0.1 cm
D.
1m
Q394 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 70 TO 72

In the figure shown blocks A and B are of mass 2 kg and 8 kg and they are connected through strings to a spring connected to ground. The blocks are in equilibrium. $(g = 10m/s^{2})$ Now the block A is pulled downwards by a force gradually increasing to 20 N. The new elongation of spring is :-
A.
2 cm
B.
4 cm
C.
20 cm
D.
40 cm
Q395 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 70 TO 72

In the figure shown blocks A and B are of mass 2 kg and 8 kg and they are connected through strings to a spring connected to ground. The blocks are in equilibrium. $(g = 10m/s^{2})$ Now the force on A is suddenly removed. The acceleration of block B becomes :-
A.
1.0 m/s
B.
2.0 m/sĀ²
C.
3.0 m/sĀ²
D.
4.0 m/sĀ²
Q396 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 73 TO 75

An object of mass m is suspended in equilibrium using a string of length $\ell$ and a spring having spring constant $K (< 2 \, mg/\ell)$ and unstreched length $\ell/2$ . Find the tension in the string in newton?
A.
$mg - \frac{k\ell}{2}$
B.
$mg - k\ell$
C.
$2mg - \frac{k\ell}{2}$
D.
$2mg - k\ell$
Q397 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 73 TO 75

An object of mass m is suspended in equilibrium using a string of length $\ell$ and a spring having spring constant $K (< 2 \, mg/\ell)$ and unstreched length $\ell/2$ . Find the acceleration of block just after cut the string?
A.
$2g - \frac{k\ell}{2m}$
B.
$g - \frac{k\ell}{2m}$
C.
$2g - \frac{k\ell}{m}$
D.
$g - \frac{k\ell}{m}$
Q398 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 73 TO 75

An object of mass m is suspended in equilibrium using a string of length $\ell$ and a spring having spring constant $K (< 2 \, mg/\ell)$ and unstreched length $\ell/2$ . What happens if $K > 2 \, mg / \ell$ ?
A.
at equilibrium tension in string is negative
B.
at equilibrium position change in length of spring is greater then $\frac{\ell}{2}$
C.
at equilibrium tension in string is zero.
D.
if cut the sting, block will accelerate in upward direction.
Q399 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 76 TO 81

When F = 2N, the frictional force between 5 kg block and ground is
A.
2 N
B.
0
C.
8 N
D.
10 N
Q400 Allen COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 76 TO 81

When $F = 2N$ , the frictional force between $10kg$ block and $5kg$ block is
A.
$2N$
B.
$15N$
C.
$10N$
D.
None