Block on a Block Problems
Trending Questions
Q. Two blocks of masses M1 and M2 are connected with a string passing over a pulley as shown in the figure. The block M1 lies on a horizontal surface. The coefficient of friction between the block M1 and the horizontal surface is μ. The system accelerates. What additional mass m should be placed on the block M1 so that the system does not accelerate?
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/877436/original_19.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/877436/original_19.png)
- M2−M1μ
- M2μ−M1
- M2−M1μ
- (M2−M1)μ
Q. A block of mass m is placed on another block of mass M, which itself is lying on a horizontal surface. The coefficient of friction between the two blocks is μ1 and that between the block of mass M and the horizontal surface is μ2. What maximum horizontal force can be applied to the lower block so that the two blocks move without separation?
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/877979/original_Dia_16.6.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/877979/original_Dia_16.6.png)
- (M+m)(μ2−μ1)g
- (M−m)(μ2−μ1)g
- (M−m)(μ2+μ1)g
- (M+m)(μ2+μ1)g
Q. For the situation shown in figure, match the following table.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1054957/original_2.2.png)
Table -1Table -2(A)Absolute acceleration of(P) 11 m/s21 kg block(B)Absolute acceleration of(Q) 6 m/s22 kg block(C)Relative acceleration between(R) 17 m/s2the two blocks(S) None
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1054957/original_2.2.png)
Table -1Table -2(A)Absolute acceleration of(P) 11 m/s21 kg block(B)Absolute acceleration of(Q) 6 m/s22 kg block(C)Relative acceleration between(R) 17 m/s2the two blocks(S) None
- A→S , B→P , C→S
- A→S , B→S , C→S
- A→P , B→P , C→P
- A→P , B→S , C→P
Q. In figure, the coefficient of static friction between the floor and block B is 0.30. The coefficient of static friction between the block B and A is 0.15. The mass of block A is m2 kg and B is m kg. What is the maximum horizontal force F in Newtons that can be applied to block B, so that the two blocks move together?
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/890572/original_qstn_7.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/890572/original_qstn_7.png)
- 1.35 mg
- 0.45 mg
- 0.675 mg
- 0.9 mg
Q. Find the maximum force F to be applied on the system shown, so that the two blocks move together. Take g=10 m/s2.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/789441/original_4.4q.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/789441/original_4.4q.png)
- 50 N
- 100 N
- 150 N
- 200 N
Q. Coefficient of friction between two blocks is μ=0.6. The blocks are given velocities in the directions shown in the figure below. Find the common velocity attained by both the blocks. [Take g=10 m/s2]
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/913884/original_06._solution.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/913884/original_06._solution.png)
- 15 m/s
- 4 m/s
- 2 m/s
- 6 m/s
Q.
Two blocks m1and m2, are acted upon by the forces F1 and F2 as shown in the fig. If there is no relative sliding between the blocks and the ground is smooth, find the magnitude of static friction between the blocks.Make necessary assumptions.
∣∣m1F1−m2F2m1+m2∣∣
∣∣m2F2−m1F1m1+m2∣∣
∣∣m2F1−m1F2m1+m2∣∣
∣∣m1F1+m2F2m1+m2∣∣
Q. A plank of mass m1=8 kg with a bar of mass m2=2 kg placed on its rough surface, lie on smooth floor of elevator ascending with an acceleration g4. The coefficient of friction is μ=15 between m1 and m2. A horizontal force F=30 N is applied to the plank. Then the acceleration of bar and the plank in the reference frame of elevator are: (g=10 m/s2)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/800263/original_13.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/800263/original_13.png)
- 3.5 m/s2, 0.5 m/s2
- 5 m/s2, 308 m/s2
- 2.5 m/s2, 258 m/s2
- 4.5 m/s2, 4.5 m/s2
Q.
Two blocks of masses M = 5 kg and m = 3 kg are placed on a horizontal surface as shown in the figure. The coefficient of friction between the blocks is 0.5 and that between the block M and the horizontal surface is 0.7. What is the maximum horizontal force F that can be applied to block M so that both the blocks move together?
4 N
16 N
24 N
96 N
Q. Two masses m1=5 kg and m2=10 kg connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of the horizontal surface is 0.15. Find the minimum weight m that should be put on top of m2 to stop the motion.
(T is tension in the string and take g=10 m/s2)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/797107/original_9.png)
(T is tension in the string and take g=10 m/s2)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/797107/original_9.png)
- 18.3 kg
- 23.3 kg
- 43.3 kg
- 10.3 kg
Q. The frictional force acting on 1 kg block will be:
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/985457/original_Picture_5.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/985457/original_Picture_5.png)
- 0.1 N
- 2 N
- 5 N
- 7.5 N
Q. A mass of 2 kg is placed on a trolley of 20 kg sliding on a smooth surface. The coefficient of friction between the mass and the surface of the trolley is 0.25. A horizontal force of 2 N is applied to the mass. The acceleration of the system and the frictional force between the mass and surface of trolley are (Take g=10 m/s2)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/796714/original_11.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/796714/original_11.png)
- 1.8 ms−2, 0.09 N
- 0.9 ms−2, 18 N
- 0.09 ms−2, 1.8 N
- 1 ms−2, 2 N
Q. For the figure shown below, the coefficient of friction between 2 kg and 4 kg block is 0.1 and between 4 kg and ground is 0.2. The graph of friction force acting on 4 kg block by the ground as a function of time is
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/797044/original_4.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/797044/original_4.png)
Q. In the figure shown below, two blocks of same mass are at rest and a horizontal force F is applied on 5 kg block towards left. If the coefficient of friction between the surfaces are 0.5 and 0.5 as shown in the figure, find the value of tension in the rope and force required just to slide the bottom block. Take g=10 m/s2.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/796771/original_download_%2822%29.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/796771/original_download_%2822%29.png)
- T=15 N, F=50 N
- T=25 N, F=50 N
- T=15 N, F=75 N
- T=25 N, F=75 N
Q. A man of mass 50 kg is pulling a rope on a plank of mass 100 kg kept on a smooth surface as shown, with force of 100 N. If both man and plank move together, find force of friction acting on man.
Given coefficient of friction between man and plank is 16.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/876570/original_10.png)
Given coefficient of friction between man and plank is 16.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/876570/original_10.png)
- 1003 N towards left
- 1003 N towards right
- 2503 N towards left
- 2503 N towards right
Q.
If satisfies , for all , , then is
Q. In the given figure, the coefficient of friction between m1 and m2 is μ and m2 and horizontal surface is zero. Choose the correct option.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/788775/original_5.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/788775/original_5.png)
- If F>μm1g, then relative acceleration is found between m1 and m2
- If F<μm1g, then no relative acceleration is found between m1 and m2
- If F>μm1g, then both bodies move togther
- (a) and (b) are correct
Q. In the figure below, masses mA=2 kg and mB=4 kg. For what minimum value of F, block A starts slipping over B (g=10 m/s2)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/823360/original_Dia_9.10.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/823360/original_Dia_9.10.png)
- 24 N
- 36 N
- 12 N
- 20 N
Q. In the arrangement shown in the figure, coefficient of friction between the two blocks is, μ=0.5. The force of friction acting between the two blocks is
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/788777/original_6.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/788777/original_6.png)
- 8 N
- 10 N
- 6 N
- 4 N
Q. In the arrangement shown in figure mA=mB=2 kg. String is massless and pulley is frictionless. Block B is resting on a smooth horizontal surface, while friction coefficient between blocks A and B is μ=0.5. The maximum horizontal force F that can be applied so that block A does not slip over the block B is. (g=10 m/s2)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/797141/original_12.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/797141/original_12.png)
- 25 N
- 40 N
- 30 N
- 20 N
Q. Find the maximum value of the magnitude of force F for which the system will move together. Take g=10 m/s2.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/788771/original_4.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/788771/original_4.png)
- 20 N
- 30 N
- 50 N
- 75 N
Q. Three large blocks each having flat surfaces are kept stationary over one another as shown in the figure. A horizontal force of 20 N acts on the middle block B, then choose the incorrect statement: (Take g=10 m/s2)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/798395/original_download_%2846%29.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/798395/original_download_%2846%29.png)
- Acceleration of the lowest block is 7 m/s2
- Friction between middle and lower blocks is 12 N
- Acceleration of the upper most block is 2 m/s2
- Friction between middle and upper blocks is 2 N
Q. A small block of mass m3=2kg of negligible size is placed on a plank of mass m2=4kg and length 4m which is further placed on a frictionless surface as shown in figure. If m1=8kg and system starts from rest,
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/471313/original_original_original_Q7.png)
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/471313/original_original_original_Q7.png)
- Time after which m3 falls from m2 is ∞
- Time after which m3 falls from m2 is 2 sec
- Velocity of m1 at 2 sec is 12 m/s
- Velocity of m2 at t = 2 sec is 11.4 m/s
Q. Find the accelerations a1, a2 and a3 of the three blocks as shown in figure, if a horizontal force of 10 N is applied on the 3 kg block. The coefficient of static friction (μ) for all contact surfaces are shown in the figure. Take g=10 m/s2.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/873865/original_rdpp7.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/873865/original_rdpp7.png)
- a1=a2=a3=56 m/s2
- a1=103 m/s2, a2=56 m/s2, a3=103 m/s2
- a1=103 m/s2, a2=103 m/s2, a3=56 m/s2
- a1=56 m/s2, a2=56 m/s2, a3=103 m/s2
Q. Find the acceleration of the two bodies (A and B), if the system shown is initially at rest.
Take g=10 m/s2.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/961119/original_original_02_S1.png)
Take g=10 m/s2.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/961119/original_original_02_S1.png)
- aA=aB=43 m/s2
- aA=43 m/s2;aB=0
- aA=0;aB=43 m/s2
- aA=2 m/s2;aB=4 m/s2
Q. Two blocks A and B of mass mA=1 kg and mB=3 kg are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F (in newtons) that can be applied on B horizontally, so that the block A does not slide over the block B is [Take , g=10 m/s2]
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/800459/original_24.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/800459/original_24.png)
Q. A block of mass m is placed on another block of mass M, which itself is lying on a horizontal surface. The coefficient of friction between the two blocks is μ1 and that between the block of mass M and the horizontal surface is μ2. What maximum horizontal force can be applied to the lower block so that the two blocks move without separation?
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/877979/original_Dia_16.6.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/877979/original_Dia_16.6.png)
- (M+m)(μ2−μ1)g
- (M−m)(μ2−μ1)g
- (M−m)(μ2+μ1)g
- (M+m)(μ2+μ1)g
Q. Find the frictional force between the two blocks. Take g=10 m/s2.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/789431/original_3.3q.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/789431/original_3.3q.png)
- 20 N
- 72 N
- 80 N
- 100 N
Q. In the given figure, the blocks of mass 2 kg and 3 kg are placed one over the other as shown. The surface are rough with coefficient of friction μ1=0.2, μ2=0.06. A force F=0.5t (where ′t′ is time in sec) is applied on upper block in the direction shown. The frictional force acting between 3 kg block and ground w.r.t. time will vary as
Take (g=10 m/s2)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/788790/original_10.png)
Take (g=10 m/s2)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/788790/original_10.png)
- None of these
Q. For the situation shown in figure, match the following table.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1054957/original_2.2.png)
Table -1Table -2(A)Absolute acceleration of(P) 11 m/s21 kg block(B)Absolute acceleration of(Q) 6 m/s22 kg block(C)Relative acceleration between(R) 17 m/s2the two blocks(S) None
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1054957/original_2.2.png)
Table -1Table -2(A)Absolute acceleration of(P) 11 m/s21 kg block(B)Absolute acceleration of(Q) 6 m/s22 kg block(C)Relative acceleration between(R) 17 m/s2the two blocks(S) None
- A→S , B→P , C→S
- A→S , B→S , C→S
- A→P , B→P , C→P
- A→P , B→S , C→P