Block on a Block Problems

Q. The coefficient of static friction between the two blocks is $0.5$ and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is _____$\text{N}$.
$(\text{Take}g=10{\text{ms}}^{-2})$

Q. In the arrangement shown in the figure, coefficient of friction between the two blocks is, $\mu =0.5$. The force of friction acting between the two blocks is

1. $8\text{N}$
2. $10\text{N}$
3. $6\text{N}$
4. $4\text{N}$

Q.

Ten one-rupee coins are put on top of each other on a table. Each coin has a mass m. Give the magnitude and direction of:
a) the force on the $7^{th}$ coin (counted from the bottom) due to all the coins on its top,
b) the force on the $7^{th}$ coin by the eighth coin,
c) the reaction of the 6th coin on the $7^{th}$ coin.

Q. Find the maximum value of $F$ such that both the blocks move together. Take $g=10{\text{m/s}}^2$.

1. $200\text{N}$
2. $100\text{N}$
3. $50\text{N}$
4. $150\text{N}$

Q. An arrangement of masses and pulleys is shown in the figure. Strings connecting masses $A$ and $B$ with the pulleys are horizontal and all pulleys and strings are light. Friction coefficient between the surface and the block $B$ is $0.2$ and between blocks $A$ and $B$ is $0.7$. The system is released from rest. Use $(g=10{\text{m/s}}^2)$. Find the magnitude of frictional force (in $\text{N}$) between block $A$ and $B$.

Q. Two blocks A and B of mass $m_A=1kg$ and $m_B=3kg$ 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 , $g=10m/s^2]$

Q.

Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force F = 600 N is applied to (i) A, (ii) B along the direction of string. What is the tension in the string in each case?

Q. In the given figure, the coefficient of friction between the two blocks is $\mu$, and all other surfaces are smooth. Find the minimum value of $F$ which will prevent slipping.

1. $\frac{(m_1+m_2)m_{1}g}{\mu m_2}$
2. $\frac{(m_1+m_2)g}{\mu m_2}$
3. $\frac{(m_1+m_2)g}{\mu m_1}$
4. $\frac{(m_1+m_2)m_{1}g}{m_2}$

Q.

Two masses $m_1$ and $m_2$ are connected by a spring of spring constant k and are placed on a friction less horizontal surface.Initially the spring is stretched through a distance $x_0$ when the system is released from rest.Find the distance moved by the two masses before they again come to rest.

Q. For the figure shown below, masses $m_1,m_2$ and $M$ are $20\text{kg},5\text{kg}$ and $50\text{kg}$ respectively. The coefficient of friction between $M$ and ground is zero. while the coefficient of friction between $M$ and $m_1$, and that between $m_2$ and ground is $0.3$. The pulleys and strings are massless. The string is perfectly horizontal between $P_1$ and $m_1$, and also between $P_2$ and $m_2$. The string is perfectly vertical between $P_1$ and $P_2$. An external horizontal force $F$ is applied on the mass $M$. Take $g=10{\text{m/s}}^2$. Let the magnitude of force of friction between $M$ and $m_1$ be $f_1$ and between $m_2$ and ground is $f_2$. For a particular $F$ it is found that $f_1=2f_2$. Choose the correct option(s).

1. Force acting on block of mass $M$ is $60N$.
2. Tension in the string is $18N$.
3. Friction force $f_1$ and $f_2$ are $30N$ and $15N$ respectively.
4. The acceleration of the block of mass $M$ is $0.3$.

Q. On a smooth horizontal table, 2 blocks of mass 20 kg and 10 kg are placed in contact. A horizontal force of 5 N is applied to the 20 kg block. With what force will this block press the 10 kg block?

Q. Two blocks $A$ and $B$ of masses $6\text{kg}$ and $3\text{kg}$ rest on a smooth horizontal surface as shown in the figure. If coefficient of friction between $A$ and $B$ is $0.4$, find the maximum horizontal force which can make them move without separation. (Take $g=10m/s^2$)

1. $72\text{N}$
2. $40\text{N}$
3. $36\text{N}$
4. $20\text{N}$

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?

1. 4 N

2. 16 N

3. 24 N

4. 96 N

Q. A small block of mass $1kg$ is placed over a plank of mass $2kg$. The length of the plank is $2m$. Coefficient of friction between the block and the plank is $0.5$ and the ground over which plank is placed is smooth. A constant force $F=30N$ is applied on the plank in horizontal direction. The time after which the block will separate from the plank is $(g=10m/s^2)$

1. $0.73s$
2. $1.2s$
3. $0.62s$
4. $1.6s$

Q. A man of mass $50\text{kg}$ is pulling a rope on a plank of mass $100\text{kg}$ kept on a smooth surface as shown, with force of $100\text{N}$. If both man and plank move together, find force of friction acting on man.
Given coefficient of friction between man and plank is $\frac{1}{6}$.

1. $\frac{100}{3}\text{N towards left}$
2. $\frac{100}{3}\text{N towards right}$
3. $\frac{250}{3}\text{N towards left}$
4. $\frac{250}{3}\text{N towards right}$

Q. The value of mass $m$ for which the $100kg$ block remains in static equillibrium is/are: (take $g=10{m/s}^2$)

1. $35kg$
2. $37kg$
3. $83kg$
4. $85kg$

Q. For the given diagram for what maximum value of force both block will move together?

1. $150\text{N}$
2. $\frac{400}{3}\text{N}$
3. $80\text{N}$
4. $200\text{N}$

Q. The frictional force acting on $1kg$ block will be:

1. $0.1\text{N}$
2. $2\text{N}$
3. $5\text{N}$
4. $7.5\text{N}$

Q. Coefficient of friction between two blocks is $\mu =0.6$. The blocks are given velocities in the directions shown in the figure below. Find the common velocity attained by both the blocks. [Take $g=10{\text{m/s}}^2$]

1. $15\text{m/s}$
2. $4\text{m/s}$
3. $2\text{m/s}$
4. $6\text{m/s}$

Q. A system of 3 blocks of masses of $10kg,20kg,30kg$ respectively, having flat surfaces of contact with coefficients of friction given in the figure are at rest initially. If a constant horizontal force of $F=100N$ is acting on $10kg$ block as shown in figure, then the magnitude of acceleration of the $20kg$ block with respect to the ground is (Take $g=10m/s^2)$

1. $1m/s^2$
2. $2m/s^2$
3. $3m/s^2$
4. $5m/s^2$

Q. Block A of mass $35\text{kg}$ is resting on a frictionless floor. Another block B of mass $7\text{kg}$ is resting on it as shown in the figure. The coefficient of static friction between the blocks is $0.5$ while kinetic friction is $0.4$. If a force of $100\text{N}$ is applied to block B, the acceleration of the block A will be $(g=10{\text{ms}}^{-2}):$

1. $0.8{\text{ms}}^{-2}$
2. $2.4{\text{ms}}^{-2}$
3. $0.4{\text{ms}}^{-2}$
4. $4.4{\text{ms}}^{-2}$

Q. Three blocks A, B and C of masses $2\text{kg},3\text{kg}$ and $4\text{kg}$ are placed as shown. Coefficient of friction between A and B is 0.5 and that between B and C is 0.1. The surface is frictionless. The maximum force $F$ in N that can be applied horizontally onto A such that the three blocks move together is (Answer upto 2 decimal places and take $g=10m{s}^{-2}$
)

Q. A block of mass $M=4\text{kg}$ is kept on a smooth horizontal plane. A bar of mass $m=1\text{kg}$ is kept on it. They are connected to a spring as shown and the spring is compressed. Then, what is the maximum compression in the spring for which the bar will not slip on the block when released, if coefficient of friction between them is $0.2$ and spring constant $=1000\text{N/m}$ (Take $g=10{\text{m/s}}^2$)

1. $1\text{cm}$
2. $1\text{m}$
3. $0.1\text{m}$
4. $10\text{cm}$

Q. A mass of $2\text{kg}$ is placed on a trolley of $20\text{kg}$ 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 $2\text{N}$ is applied to the mass. The acceleration of the system and the frictional force between the mass and surface of trolley are (Take $g=10m/s^2$)

1. $1.8{\text{ms}}^{-2},0.09\text{N}$
2. $0.9{\text{ms}}^{-2},18\text{N}$
3. $0.09{\text{ms}}^{-2},1.8\text{N}$
4. $1{\text{ms}}^{-2},2\text{N}$

Q. A block of mass $2\text{kg}$ is resting over another block of mass $6\text{kg}$. $2\text{kg}$ block is connected to one end of a string fixed to a vertical wall as shown. If the coefficient of friciton between the blocks is $0.4$, the force required to pull out the $6\text{kg}$ block with an acceleration of $1.5{\text{m/s}}^2$ will be $(g=10{\text{ms}}^{-2})$

1. $17\text{N}$
2. $9\text{N}$
3. $8\text{N}$
4. $7\text{N}$

Q. What should be the maximum value of $M$ so that the $4\text{kg}$ block does not slip over the $5\text{kg}$ block: (Take $g=10{\text{m/s}}^2)$

1. $12\text{kg}$
2. $8\text{kg}$
3. $10\text{kg}$
4. $6\text{kg}$

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 ${\mu }_1$ and that between the block of mass $M$ and the horizontal surface is ${\mu }_2$. What maximum horizontal force can be applied to the lower block so that the two blocks move without separation?

1. $(M-m)({\mu }_2+{\mu }_1)g$
2. $(M+m)({\mu }_2-{\mu }_1)g$
3. $(M-m)({\mu }_2-{\mu }_1)g$
4. $(M+m)({\mu }_2+{\mu }_1)g$

Q. Block A, as shown in the figure weighs $2N$ and block B weighs $6N$. The coefficient of kinetic friction between all surfaces is 0.25. Find the magnitude of the horizontal force necessary to drag block B to the left at constant speed if A and B are connected by a light, flexible cord passing around a fixed, frictionless pulley.

1. $2N$
2. $3N$
3. $5N$
4. $6N$

Q. Block $A$ is placed on block $B$, whose mass is greater than that of $A$. There is friction between the blocks, while the ground is smooth. A horizontal force $P$, increasing linearly with time, begins to act on $A$. The accelerations $a_1$ and $a_2$ of $A$ and $B$ respectively are plotted against time ($t$). Choose the correct graph.

1. 
2. 
3. 
4. 

Q. Find the frictional force between the two blocks. Take $g=10{\text{m/s}}^2$.

1. $6\text{N}$
2. $28\text{N}$
3. $30\text{N}$
4. $70\text{N}$