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629 Questions Start Allen Test
All Exams Allen Objective Errorless
Q401 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
Three masses $M_{1}$ , $M_{2}$ and $M_{3}$ are lying on a frictionless table. The masses are connected by massless threads as shown. The mass $M_{3}$ is pulled by a constant force F as shown. The tension in the thread between masses $M_{2}$ and $M_{3}$ is image.png
A.
$\frac{F}{2}$
B.
$\frac{F}{3}$
C.
$\frac{F}{4}$
D.
$\frac{F}{6}$
Q402 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
Three blocks are connected as shown in fig. on a horizontal frictionless table. If $M_{1} = 1$ kg, $M_{2} = 8$ kg, $M_{3} = 27$ kg and F = 36N, Then T' will be :-
A.
$18\mathrm{N}$
B.
$8\mathrm{N}$
C.
$35\mathrm{N}$
D.
$27\mathrm{N}$
Q403 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
Three blocks of masses $m_{1}$ , $m_{2}$ and $m_{3}$ are connected by massless strings as shown in the figure on a frictionless table. Forces of 10 N and 40 N are applied on them as shown in diagram. If $m_{1} = 10kg$ , $m_{2} = 6kg$ and $m_{3} = 4kg$ , then tension $T_{2}$ will be: image.png
A.
10 N
B.
20 N
C.
25 N
D.
35 N
Q404 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
Two bodies A and B of masses 10 kg and 15 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. If T represents the tension in the string when a horizontal force F = 500 N is applied to A (as shown in figure 1) and T' be the tension when F = 750 N is applied to B (figure2), then which of the following is true?
A.
$\mathrm{T} = \mathrm{T}' = 500\mathrm{N}$
B.
$\mathrm{T} = \mathrm{T}' = 250\mathrm{N}$
C.
$\mathrm{T} = 300\mathrm{N},\mathrm{T}' = 200\mathrm{N}$
D.
$\mathrm{T} = 300\mathrm{N},\mathrm{T}' = 300\mathrm{N}$
Q405 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
The surface shown in diagram is frictionless and $T_{1}$ is 30 N, then the value of F is :-
A.
$30\mathrm{N}$
B.
$60\mathrm{N}$
C.
$120\mathrm{N}$
D.
$69.36\mathrm{N}$
Q406 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
Two blocks of masses 5 kg and 3 kg connected by a rope of mass 2 kg are resting on a frictionless floor as shown in the following figure. If a constant force of 50 N is applied to 5 kg block, then the tension in the rope at points A, B and C are respectively given by:
A.
7.5N, 10N, 12.5N
B.
12.5N, 10N, 7.5N
C.
20N, 20N, 20N
D.
50N, 50N, 50N
Q407 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
Two blocks of masses 10 kg and 5 kg are connected from a massless string as shown in figure. The system is pulled up with a force of 210 N, then the acceleration of the system is :-
A.
$14\mathrm{m / s^2}$
B.
$11\mathrm{m / s^2}$
C.
$4\mathrm{m / s^2}$
D.
zero
Q408 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
A block of weight 40 N is 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
Q409 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
A monkey of mass 15 kg is holding a vertical rope. The rope will not break when a mass of 30 kg is suspended from it but will break if the mass exceeds 30 kg what is the maximum acceleration with which the monkey can climb up along the rope? (g = 10 m/sĀ²)
A.
15 m/sĀ²
B.
10 m/sĀ²
C.
25 m/sĀ²
D.
20 m/sĀ²
Q410 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
A uniform rope of length L resting on a frictionless horizontal surface is pulled at one end by a force F. What is the tension in the rope at a distance $\ell$ from the end where the force is applied.
A.
F
B.
$F(1+\ell/L)$
C.
F/2
D.
$F(1-\ell/L)$
Q411 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
A string of length L and mass M is lying on a horizontal table. A force F is applied at one of its ends. Tension in the string at a distance x from the end other than at which force is applied is
A.
Zero
B.
Fx/L
C.
F(L - x)/L
D.
F(L - x)/M
Q412 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
A block of mass m is pulled along a horizontal frictionless surface by a rope of mass m. If a force F is applied at one end of the rope, the tension at the mid-point of the rope is :-
A.
$\frac{\text{F}}{2}$
B.
$\frac{3\text{F}}{4}$
C.
$\frac{\text{F}}{4}$
D.
$\frac{\text{F}}{3}$
Q413 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
Two particles of masses m and 2M (M > m) are connected by a cord that passes over a massless and frictionless pulley. The tension T in the string and the acceleration a of the particles is:
A.
$T = \frac{2mM}{(M - m)}g; a = \left(\frac{M - m}{M + m}\right)g$
B.
$T = \frac{4mM}{(2M + m)}g; a = \left(\frac{2M - m}{2M + m}\right)g$
C.
$T = \left(\frac{2M - m}{2M + m}\right)g; a = \left(\frac{4mM}{M + m}\right)g$
D.
$T = \left(\frac{2Mm}{2M + m}\right)g; a = \left(\frac{4mM}{2M + m}\right)g$
Q414 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
What will be the acceleration of the blocks if they are set free to move? (g = acceleration due to gravity)
A.
g
B.
g/2
C.
g/3
D.
g/4
Q415 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
Three blocks each of mass 5 kg are hanging on a string passing over a fixed pulley as shown in fig. What is the tension in the string connecting blocks A and B.
A.
Zero
B.
$33.3\mathrm{N}$
C.
$66.67\mathrm{N}$
D.
$50\mathrm{N}$
Q416 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
In the arrangement shown in the figure, the pulley has a mass 3m. Neglecting friction on the contact surface, the force exerted by the supporting rope AB on the ceiling is :-
A.
5.67mg
B.
3mg
C.
4mg
D.
2.67mg
Q417 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
The pulley arrangements shown in the figure are ideal, the mass of the rope being negligible. In case (a) mass m is lifted by attaching a mass of 2m to the other end of the rope. In case (b) the mass m is connected with an another mass m which is pulling by a rope with a constant downward force F = mg, where g is the acceleration due to gravity. The acceleration of mass m in case (a) is :-
(a)

(b)
A.
Zero
B.
More than that in case (b)
C.
Less than that in case (b)
D.
Equal to that in case (b)
Q418 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
In the fig. given below masses m and m' are tied with a thread passing over a pulley, m' is on a frictionless horizontal surface. If acceleration due to gravity is g, the acceleration of m in this arrangement will be :-
A.
g
B.
$\mathrm{m}'\mathrm{g} / (\mathrm{m} + \mathrm{m}')$
C.
$\mathrm{mg / (m + m^{\prime})}$
D.
$\mathrm{mg} / (\mathrm{m} - \mathrm{m}')$
Q419 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
Two bodies of masses 15 kg and 5 kg are arranged in two different ways as shown in fig. (A) and (B). If the pulleys and the table are perfectly smooth, the acceleration of the 5 kg body in case (A) and (B) are respectively :-
A.
3g/4 and g/2
B.
g/5 and g/2
C.
g/2 and 3g/4
D.
15g/2 and g/5
Q420 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
A constant force $F = m_{1}g/2$ is applied on the block of mass $m_{2}$ as shown in figure. The string and the pulley are light and the surface of the table is smooth. Find the acceleration of $m_{2}$
A.
$\frac{\mathbf{m}_2\mathbf{g}}{\mathbf{m}_1 + \mathbf{m}_2}$
B.
$\frac{\mathbf{m}_1\mathbf{g}}{\mathbf{m}_1 + \mathbf{m}_2}$
C.
$\frac{\mathrm{m}_1\mathrm{g}}{2(\mathrm{m}_1 + \mathrm{m}_2)}$
D.
$\frac{\mathrm{m}_2\mathrm{g}}{2(\mathrm{m}_1 + \mathrm{m}_2)}$
Q421 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
Two bodies A (20 kg) and B (30 kg) tied with a light string are placed on a frictionless table. A force F acting at B pulls this system with an acceleration of $3 \, ms^{-2}$ . The tension in the string is:
A.
60 N
B.
120 N
C.
90 N
D.
140 N
Q422 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
Consider the system as shown in the figure. The pulley and the string are light and all the surfaces are frictionless. The tension in the string is $(\mathrm{g} = 1 0 \mathrm{m} / \mathrm{s} ^ {2}) $
A.
zero
B.
1N
C.
2N
D.
5N
Q423 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
Three masses of 1 kg, 6 kg and 3 kg are connected to each other with threads and are placed on a table as shown in figure. The ratio $\frac{T_{1}}{T_{2}}$ is: $(Take\ g = 10\ m/s^{2})$
A.
1:1
B.
2:1
C.
1:2
D.
3:1
Q424 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
Two blocks of mass 3M and 4M are resting on a frictionless inclined planes as shown in fig. then
A.
The block A moves down the plane
B.
The block B moves down the plane
C.
Both the blocks remain at rest
D.
Both the blocks move down the plane.
Q425 Allen CONNECTED BY STRINGS, PULLEY SYSTEM MCQ
The acceleration of the block shown in figure :-
A.
0
B.
$\frac{\mathrm{g}\sin\theta}{2}$
C.
$\frac{2\mathrm{g}\sin\theta}{3}$
D.
$2\mathrm{g}\sin\theta$