Block on a Block Problems

Q.

Two masses $m_1=5kg$ and $m_2=10kg$, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction on a horizontal surface is 0.15. The minimum weight m that should be put on top of $m_2$ to stop the motion is.

1. 43.3 kg

2. 10.3 kg

3. 18.3 kg

4. 27.3 kg

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. Find the acceleration of the two blocks of mass $4\text{kg}$ & $5\text{kg},$ if a force of $40\text{N}$ is applied on $4\text{kg}$ block. Friction coefficient between the respective surfaces are shown in figure. (take $g=10{\text{m/s}}^2$).

1. $a_2=a_1=5{\text{m/s}}^2$
2. $a_1=a_2=\frac{13}{9}{\text{m/s}}^2$
3. $a_1=0,a_2=5{\text{m/s}}^2$
4. $a_2=0,a_1=\frac{13}{9}{\text{m/s}}^2$

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.

Block A is kept on top of block B and moves leftwards with respect to B. Assume the friction to be present between the blocks. The direction of friction force on A by B, will be?

1. ↘

2. ↙

3. ←

4. →

Q. Find the acceleration of the $3m$ block when the system is released from rest. All other surfaces are smooth except between $m$ and $2m$. Take $g=10m/s^2$

1. $a=3m/s^2$
2. $a=3.5m/s^2$
3. $a=5m/s^2$
4. $a=5.4m/s^2$

Q. Two blocks of masses $2\text{kg}$ and $4\text{kg}$ are arranged as shown in figure. Then, find the maximum value of force $F$, for which both blocks will move together.

1. $10\text{N}$
2. $30\text{N}$
3. $20\text{N}$
4. $40\text{N}$

Q.

In the adjoining figure, the coefficient of friction between wedge (of mass M) and block (of mass m) is $\mu$.

Find the minimum horizontal force F required to keep the block stationary with respect to wedge.

1. None

2. 

3. 

4. 

Q. In the figure shown below, coefficient of friction between the $3\text{kg}$ block and ground varies with time as $\mu =0.02t$ and the force acting on the block is given by $F=5t$. Then, work done by the friction force on the $2\text{kg}$ block up to $5\text{sec}$, from the frame of reference of the $3\text{kg}$ block is:
[Take $g=10{\text{m/s}}^2$]

Q. A circular racetrack of radius $300m$ is banked at angle of ${15}^o$ If the coefficient of friction between the wheels of a race car and the road is $0.2$ what is the (a) optimum speed of the race car to avoid wear and tear on its tyres and maximum permissible speed to avoid slipping?

Q. Block B of mass $2\text{kg}$ is placed on smooth horizontal plane. Block A of mass $1\text{kg}$ is placed on block B. The coefficient of friction between A and B is 0.40. The block A is imparted a velocity $16\text{m/s}$ at t = 0. Find the time at which momentum of the two blocks are equal (in seconds). $(g=10{\text{m/s}}^2)$.

Q. a point particle of mass m moves along the uniformly rough track PQR the cofficient of friction between the particle and the rough track equals μ.the particle is released from rest , from the point p and it come to rest at a point R the energies lost by the ball over tthe parts PQ and QR of the track are equal to each other and no energy is lost when particle change direction from PQ to qR the values of the cofficient of friction μ and dis†an ce

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. 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 vehicle of mass $1000kg$ is moving with a velocity of $15m{s}^{-1}$. It is brought to rest by applying brakes and locking the wheels. If the sliding friction between the tires and the rod is $6000N$, distance moved by the vehicle before coming to rest is:

1. 18.75 m
2. 37.5 m
3. 75 m
4. 15 m

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. Find the acceleration of the $3m$ block when the system is released from rest. All other surfaces are smooth except between $m$ and $2m$. Take $g=10m/s^2$

1. $a=3m/s^2$
2. $a=3.5m/s^2$
3. $a=5m/s^2$
4. $a=5.4m/s^2$

Q. Two blocks of masses $2\text{kg}$ and $4\text{kg}$ are arranged as shown in figure. Then, find the maximum value of force $F$, for which both blocks will move together.

1. $10\text{N}$
2. $30\text{N}$
3. $20\text{N}$
4. $40\text{N}$

Q. A block $A\left(5\text{kg}\right)$ rests over another block $B\left(3\text{kg}\right)$ placed over a smooth horizontal surface. There is friction between $A$ and $B$. A horizontal force $F_1$ gradually increasing from zero to a maximum is applied to $A$ so that the blocks move together without relative motion. Instead of this another horizontal force $F_2$, gradually increasing from zero to a maximum is applied to $B$ so that the blocks move together without relative motion. Then

1. $F_1\text{(max)}=F_2\text{(max)}$
2. $F_1\text{(max)}>F_2\text{(max)}$
3. $F_1\text{(max)}<F_2\text{(max)}$
4. $F_1\text{(max)}:F_2\text{(max)}=5:3$

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

Q. In the figure shown below, a horizontal force $F$ is applied on $5kg$ block towards left. If the coefficient of friction between the surfaces are $0.8$ and $0.8$ as shown in the figure., find the value of tension in the rope and force required just to slide the $5kg$ block under the $10kg$ block. Take $g=10m/s^2$.

1. $T=50\text{N},F=120\text{N}$
2. $T=62.5\text{N},F=140\text{N}$
3. $T=75\text{N},F=160\text{N}$
4. $T=87.5\text{N},F=140\text{N}$

Q. In figure both the pulleys are massless and frictionless. A force $F$ (of any possible magnitude) is applied in horizontal direction. There is no friction between $M$ and the ground. ${\mu }_1$ and ${\mu }_2$ are coefficients of friction as shown between the blocks. Column I gives the different relations between ${\mu }_1$ and ${\mu }_2$ and Column II is regarding the motion of $M$. Match the columns.


$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{i. If}{\mu }_1={\mu }_2=0& \text{a. may accelerate towards right}\\ \text{ii. If}{\mu }_1={\mu }_2\ne 0& \text{b. may accelerate towards left}\\ \text{iii. If}{\mu }_1>{\mu }_2& \text{c. does not accelerate}\\ \text{iv. If}{\mu }_1<{\mu }_2& \text{d. may or may not accelerate}\end{array}$

1. $\text{(i- c; ii- c; iii- b, d; iv- a, d)}$
2. $\text{(i-c; ii- b; iii- c, d; iv- a, d)}$
3. $\text{(i- b, d; ii- c; iii- b, d; iv- a, d)}$
4. $\text{(i- a, c; ii- c; iii- d; iv- d)}$

Q. A small block of mass $m=2kg$ is projected on a larger block of $20kg$ and of length $20\text{metres}$, with a velocity of $vm/s$ as shown in the figure. The coefficient of friction between the two blocks is $1.2$, while between the lower block and ground is $0.1$. The time taken by the small block to fall off the larger block is (Take $g=10m/s^2$)

1. $2.5s$
2. $4s$
3. $3s$
4. $2s$

Q. In the diagram shown below the coefficient of friction between $2\text{kg}$ and $4\text{kg}$ block is $0.1$ and between $4\text{kg}$ and ground is $0.2$. Find the force of friction on $2\text{kg}$ block at time $t=0.5$ second.

1. $2\text{N towards left}$
2. $1\text{N towards right}$
3. $1\text{N towards left}$
4. $0\text{N}$

Q. Find the maximum force $F$ to be applied for the system shown, so that the two blocks move together. Take $g=10{\text{m/s}}^2$.

1. $1.5\text{N}$
2. $25\text{N}$
3. $5\text{N}$
4. $2.5\text{N}$

Q. A vehicle of mass $m$ is driven along an un-banked curved path of radius of curvature $r$ with a speed $v$. If $\mu$ is necessary minimum coefficient of friction between tyres of vehicle and road so that the vehicle does not skid, then:

1. $\mu \propto \frac{1}{v^2}$
2. $\mu \propto r$
3. $\mu \propto v^2$
4. $\mu \propto \frac{1}{r}$

Q. Find the acceleration of the two bodies ($A$ and $B$), if the system shown is initially at rest.
Take $g=10{\text{m/s}}^2$.

1. $a_A=a_B=\frac{4}{3}{\text{m/s}}^2$
2. $a_A=\frac{4}{3}{\text{m/s}}^2;a_B=0$
3. $a_A=0;a_B=\frac{4}{3}{\text{m/s}}^2$
4. $a_A=2{\text{m/s}}^2;a_B=4{\text{m/s}}^2$

Q. Find the accelerations $a_1,a_2$ and $a_3$ of the three blocks as shown in figure, if a horizontal force of $10\text{N}$ is applied on the $3\text{kg}$ block. The coefficient of static friction ($\mu$) for all contact surfaces are shown in the figure. Take $g=10{\text{m/s}}^2$.

1. $a_1=a_2=a_3=\frac{5}{6}{\text{m/s}}^2$
2. $a_1=\frac{10}{3}{\text{m/s}}^2,a_2=\frac{5}{6}{\text{m/s}}^2,a_3=\frac{10}{3}{\text{m/s}}^2$
3. $a_1=\frac{10}{3}{\text{m/s}}^2,a_2=\frac{10}{3}{\text{m/s}}^2,a_3=\frac{5}{6}{\text{m/s}}^2$
4. $a_1=\frac{5}{6}{\text{m/s}}^2,a_2=\frac{5}{6}{\text{m/s}}^2,a_3=\frac{10}{3}{\text{m/s}}^2$

Q. A circular road of radius r is banked for a speed v=40km/hr. A car of mass m attempts to go on the circular road. The friction coefficient between the tyre and the road is negligible.

1. The car cannot make a turn without skidding
2. if the car turns at a speed less than 40 km/hr, it will slip down.
3. If the car turns at the correct speed of 40 km/hr, the force by the road on the car is equal to ${mv}^2/r$
4. If the car turns at the correct speed of 40 km/hr, the force by the road on the car is greater than mg as well as greater than ${mv}^2/r$

Q. A system consists of block A and B of same mass $5kg$ and connected to the pulley as shown in figure. Find the relative acceleration with which they will move?
(Take $g=10m/s^2$)

1. $8m/s^2$
2. $5m/s^2$
3. $4m/s^2$
4. $16m/s^2$