Q851
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 9
A block of mass m slides down an inclined plane of elevation angle $\alpha$ . The incline is fixed end to end in an elevator of base length l. Assume that initially the particle is at the top of the incline. Based on the above facts, answer the following questions.
If the elevator moves with constant velocity, then the time taken by the block to reach the bottom of the incline is
A.
$\sqrt{\frac{2l}{g\sin(2\alpha)}}$
B.
$\sqrt{\frac{2l}{g\cos\alpha}}$
C.
$\sqrt{\frac{2l}{g}}$
D.
$\sqrt{\frac{4l}{g\sin(2\alpha)}}$
Q852
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 10
A block of mass m slides down a smooth incline of mass M and length l, solely as a result of the force of gravity. The incline is placed on a smooth horizontal table as shown in figure. Let us denote the coordinate system relative to the table as S and the coordinate system relative to the incline as $S'$ .
The acceleration of $m$ in the $S'$ frame is
The acceleration of $m$ in the $S'$ frame is
A.
$\frac{(M + m)g\sin\theta}{M + m\sin^2\theta}$
B.
$\frac{(M + m)g\sin\theta}{m - M\sin^2\theta}$
C.
$\frac{(M - m)g\sin\theta}{M + m\sin^2\theta}$
D.
$\frac{(M + m)g\sin\theta}{M + m\sin\theta}$
Q853
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 10
A block of mass m slides down a smooth incline of mass M and length l, solely as a result of the force of gravity. The incline is placed on a smooth horizontal table as shown in figure. Let us denote the coordinate system relative to the table as S and the coordinate system relative to the incline as $S'$ .
The acceleration of the incline in the $S$ frame
The acceleration of the incline in the $S$ frame
A.
$\left(\frac{mg\sin\theta\cos\theta}{M - m\sin^2\theta}\right)$
B.
$\left(\frac{mg\sin\theta\cos\theta}{M + m\sin^2\theta}\right)$
C.
$\left(\frac{Mg\sin\theta\cos\theta}{M - m\sin^2\theta}\right)$
D.
$\left(\frac{Mg\sin\theta\cos\theta}{M + m\sin^2\theta}\right)$
Q854
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 10
A block of mass m slides down a smooth incline of mass M and length l, solely as a result of the force of gravity. The incline is placed on a smooth horizontal table as shown in figure. Let us denote the coordinate system relative to the table as S and the coordinate system relative to the incline as $S'$ .
The force exerted by the small $m$ on the wedge of mass $M$
The force exerted by the small $m$ on the wedge of mass $M$
A.
$mg \cos \theta$
B.
$\frac{Mmg \cos \theta}{M + m \sin^2 \theta}$
C.
$\frac{mg}{\cos \theta}$
D.
None of these
Q855
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 11
A heavy block of mass 250 kg is being pulled up an inclined plane of angle $30^{\circ}$ by means of a wire passing over a pulley of radius 5 cm and connected to a motor as shown in the figure. The power output of the motor is 5 kW and the block moves up with a constant velocity of $2 \, ms^{-1}$ . Based on the information provided, answer the following questions.
The coefficient of friction between the block and the inclined surface is
The coefficient of friction between the block and the inclined surface is
A.
$\frac{1}{\sqrt{2}}$
B.
$\frac{1}{\sqrt{3}}$
C.
$\frac{1}{2}$
D.
$\frac{1}{\sqrt{5}}$
Q856
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 11
A heavy block of mass 250 kg is being pulled up an inclined plane of angle $30^{\circ}$ by means of a wire passing over a pulley of radius 5 cm and connected to a motor as shown in the figure. The power output of the motor is 5 kW and the block moves up with a constant velocity of $2 \, ms^{-1}$ . Based on the information provided, answer the following questions.
Contact force between the inclined plane and heavy block
Contact force between the inclined plane and heavy block
A.
1250 N
B.
25000 N
C.
5000 N
D.
2500 N
Q857
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 11
A heavy block of mass 250 kg is being pulled up an inclined plane of angle $30^{\circ}$ by means of a wire passing over a pulley of radius 5 cm and connected to a motor as shown in the figure. The power output of the motor is 5 kW and the block moves up with a constant velocity of $2 \, ms^{-1}$ . Based on the information provided, answer the following questions.
Tension in the string
Tension in the string
A.
250 N
B.
1250 N
C.
2500 N
D.
5000 N
Q858
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 11
A heavy block of mass 250 kg is being pulled up an inclined plane of angle $30^{\circ}$ by means of a wire passing over a pulley of radius 5 cm and connected to a motor as shown in the figure. The power output of the motor is 5 kW and the block moves up with a constant velocity of $2 \, ms^{-1}$ . Based on the information provided, answer the following questions.
Frictional force acts on the block
Frictional force acts on the block
A.
12.5 N
B.
125 N
C.
1250 N
D.
12500 N
Q859
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 12
A bead of mass m is attached to one end of a spring of natural length R and spring constant $k = \frac{(\sqrt{3} + 1)mg}{R}$ . The other end of the spring is fixed at point A on a smooth vertical ring of radius R as shown in figure. Based on the information provided, answer the following questions.
The normal reaction at $B$ just after it is released to move is
The normal reaction at $B$ just after it is released to move is
A.
$\frac{mg}{2}$
B.
$\sqrt{3} mg$
C.
$3\sqrt{3} mg$
D.
$\frac{3\sqrt{3} mg}{2}$
Q860
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 12
A bead of mass m is attached to one end of a spring of natural length R and spring constant $k = \frac{(\sqrt{3} + 1)mg}{R}$ . The other end of the spring is fixed at point A on a smooth vertical ring of radius R as shown in figure. Based on the information provided, answer the following questions.
Tangential acceleration of the bead just after it is released is
Tangential acceleration of the bead just after it is released is
A.
$\frac{g}{2}$
B.
$\frac{g}{4}$
C.
$\frac{2g}{3}$
D.
$\frac{3g}{4}$
Q861
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 13
A painter of mass 100 kg is raising himself and the crate (such an arrangement is called Bosun's chair) on which he stands as shown. When he pulls the rope the force exerted by him on the crate's floor is 450 N. If the crate weighs 25 kg then, based on the information provided, answer the following questions.
The acceleration of the system (painter + crate) is
The acceleration of the system (painter + crate) is
A.
$22 \, ms^{-2}$ , up
B.
$2 \, ms^{-2}$ , down
C.
$2 \, ms^{-2}$ , down
D.
$22 \, ms^{-2}$ , down
Q862
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 13
A painter of mass 100 kg is raising himself and the crate (such an arrangement is called Bosun's chair) on which he stands as shown. When he pulls the rope the force exerted by him on the crate's floor is 450 N. If the crate weighs 25 kg then, based on the information provided, answer the following questions.
The tension in the cable supporting the cabin is
The tension in the cable supporting the cabin is
A.
500 N
B.
1000 N
C.
1250 N
D.
750 N
Q863
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 13
A painter of mass 100 kg is raising himself and the crate (such an arrangement is called Bosun's chair) on which he stands as shown. When he pulls the rope the force exerted by him on the crate's floor is 450 N. If the crate weighs 25 kg then, based on the information provided, answer the following questions.
Assuming the painter to be of mass $M$ , crate to be of mass $m$ , then the system will be in equilibrium when the painter holds the rope with a force given by
Assuming the painter to be of mass $M$ , crate to be of mass $m$ , then the system will be in equilibrium when the painter holds the rope with a force given by
A.
$(m + M)g$
B.
$(M - m)g$
C.
$\frac{1}{2}(M + m)g$
D.
$\frac{1}{2}(M - m)g$
Q864
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 14
A particle of mass m is suspended by the two strings a and b each of length l as shown. Based on this simple information, answer the following questions.
In equilibrium, tension in the string $a$ is
In equilibrium, tension in the string $a$ is
A.
$2mg$
B.
$\sqrt{3} mg$
C.
$mg$
D.
$3mg$
Q865
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 14
A particle of mass m is suspended by the two strings a and b each of length l as shown. Based on this simple information, answer the following questions.
In equilibrium, tension in the string $b$ is
In equilibrium, tension in the string $b$ is
A.
2mg
B.
$\sqrt{3}mg$
C.
mg
D.
3mg
Q866
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 14
A particle of mass m is suspended by the two strings a and b each of length l as shown. Based on this simple information, answer the following questions.
If the string $a$ is now burned then the speed of the ball just before it collides with the wall is
If the string $a$ is now burned then the speed of the ball just before it collides with the wall is
A.
$\sqrt{\frac{gl}{2}}$
B.
$\sqrt{2gl}$
C.
$\sqrt{gl}$
D.
$\frac{\sqrt{gl}}{2}$
Q867
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 15
The system shown in the figure is in equilibrium. The masses $m_{1}$ and $m_{2}$ are 2 kg and 8 kg respectively, the springs have spring constants $k_{1}=50\ Nm^{-1}$ and $k_{2}=70\ Nm^{-1}$ and the compression in second spring is 0.5 m. Assuming both the springs to have the same natural length, answer the following questions.
The extension in first spring is
The extension in first spring is
A.
1.3 m
B.
-0.5 m
C.
0.5 m
D.
0.9 m
Q868
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 15
The system shown in the figure is in equilibrium. The masses $m_{1}$ and $m_{2}$ are 2 kg and 8 kg respectively, the springs have spring constants $k_{1}=50\ Nm^{-1}$ and $k_{2}=70\ Nm^{-1}$ and the compression in second spring is 0.5 m. Assuming both the springs to have the same natural length, answer the following questions.
The tension in the string is
The tension in the string is
A.
45 N
B.
40 N
C.
50 N
D.
38 N
Q869
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 15
The system shown in the figure is in equilibrium. The masses $m_{1}$ and $m_{2}$ are 2 kg and 8 kg respectively, the springs have spring constants $k_{1}=50\ Nm^{-1}$ and $k_{2}=70\ Nm^{-1}$ and the compression in second spring is 0.5 m. Assuming both the springs to have the same natural length, answer the following questions.
The acceleration of the mass $m_{1}$ , when spring $k_{1}$ is cut, is
The acceleration of the mass $m_{1}$ , when spring $k_{1}$ is cut, is
A.
zero
B.
2.5 ms $^{-2}$
C.
3 ms $^{-2}$
D.
None of these
Q870
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 16
A block of mass $M$ is placed on a horizontal surface and it is tied through an inextensible string to a block of mass $m$ , as shown in figure. A block of mass $m_{0}$ is also placed on M. Based on the information provided, answer the following questions.
If there is no friction between any two surfaces in contact, then
If there is no friction between any two surfaces in contact, then
A.
a downward acceleration of the block m is $\frac{mg}{m + m_{0} + M}$
B.
the acceleration of $m_{0}$ is zero
C.
the tension in the string is Mg < T < mg
D.
All the above
Q871
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 16
A block of mass $M$ is placed on a horizontal surface and it is tied through an inextensible string to a block of mass $m$ , as shown in figure. A block of mass $m_{0}$ is also placed on M. Based on the information provided, answer the following questions.
If a friction force exist between block $M$ and the horizontal surface with the coefficient of friction $\mu$ , then the minimum value of $\mu$ (call it as $\mu_{\min}$ ) for which the block $m$ remains stationary is
If a friction force exist between block $M$ and the horizontal surface with the coefficient of friction $\mu$ , then the minimum value of $\mu$ (call it as $\mu_{\min}$ ) for which the block $m$ remains stationary is
A.
$\frac{m}{M}$
B.
$\frac{m}{M + m_0}$
C.
$\frac{M + m_0}{M}$
D.
$\frac{M}{M + m_0}$
Q872
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 16
A block of mass $M$ is placed on a horizontal surface and it is tied through an inextensible string to a block of mass $m$ , as shown in figure. A block of mass $m_{0}$ is also placed on M. Based on the information provided, answer the following questions.
If $\mu < \mu_{\min}$ (the minimum friction required to keep the block $m$ stationary), then the downward acceleration of $m$ is
If $\mu < \mu_{\min}$ (the minimum friction required to keep the block $m$ stationary), then the downward acceleration of $m$ is
A.
$\left[\frac{m - \mu M}{m + M}\right]g$
B.
$\left[\frac{m - \mu(m_0 + M)}{m + m_0 + M}\right]g$
C.
$\left[\frac{m - \mu(m_0 + M)}{m + M}\right]g$
D.
$\left[\frac{m - \mu M}{m + m_0 + M}\right]g$
Q873
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 17
ABCD is a vertical frame of mass M. Two strings between block of mass m and frame are ideal and lies in vertical plane. The frame ABCD is placed on horizontal smooth surface and a horizontal force F is applied as shown. Points P and Q are in same vertical line and two strings are of equal length.
Based on the above facts, answer the following questions.
Minimum force F required to make both string tight is
Based on the above facts, answer the following questions.
Minimum force F required to make both string tight is
A.
$Mg \tan \theta$
B.
$Mg \cot \theta$
C.
$(m + M)g \tan \theta$
D.
$(m + M)g \cot \theta$
Q874
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 17
ABCD is a vertical frame of mass M. Two strings between block of mass m and frame are ideal and lies in vertical plane. The frame ABCD is placed on horizontal smooth surface and a horizontal force F is applied as shown. Points P and Q are in same vertical line and two strings are of equal length.
Based on the above facts, answer the following questions.
If the lower string is just tight then tension in the upper string is
Based on the above facts, answer the following questions.
If the lower string is just tight then tension in the upper string is
A.
$\frac{mg}{\sin\theta}$
B.
$\frac{mg}{\cos\theta}$
C.
$mg \sin \theta$
D.
$mg \cos \theta$
Q875
Advance
LINKED COMPREHENSION TYPE QUESTIONS
MCQ
Comprehension Passage: Comprehension - 17
ABCD is a vertical frame of mass M. Two strings between block of mass m and frame are ideal and lies in vertical plane. The frame ABCD is placed on horizontal smooth surface and a horizontal force F is applied as shown. Points P and Q are in same vertical line and two strings are of equal length.
Based on the above facts, answer the following questions.
The value of force $F$ for which the tension in upper string becomes twice than tension in lower string is
Based on the above facts, answer the following questions.
The value of force $F$ for which the tension in upper string becomes twice than tension in lower string is
A.
$3(m + M)g\tan \theta$
B.
$2(m + M)g\tan \theta$
C.
$4(m + M)g\tan \theta$
D.
None of these