Inclined Planes

Q. ASSERTION : The time of ascent for a body projected to move up a rough inclined plane is less than the time of descent.
REASON : The retardation for upward motion is more than the acceleration for downward motion.

1. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
2. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
3. Assertion is true but Reason is false
4. Both Assertion and Reason are false

Q. A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the inclined plane are same but not sufficient to allow pure rolling. The time taken to reach bottom will be least for

1. Solid sphere
2. Hollow sphere
3. Disc
4. All of the above reach ground at same time

Q.

A force of 100 N needs to be applied parallel to a smooth inclined plane just to hold a body on it. The angle of inclination of the inclined plane is ${30}^{\circ }$. How much horizontal force needs to be applied to do the same?

1. 50 N

2. 87 N

3. 100 N

4. 115 N

Q. System is released from rest. Find speed of the blocks after 2 seconds.

1. $4.2m/s$
2. $5.6m/s$
3. $2.4m/s$
4. $4.8m/s$

Q. A block of mass $m=2\text{kg}$ is resting on a rough inclined plane of inclination ${30}^{\circ }$ as shown in figure. The coefficient of friction between the block and the plane is $\mu =0.5$. What minimum force $F$ should be applied on the block as shown in figure, so that the block does not slip on the plane?( $g=10{\text{ms}}^{-2})$

1. Zero
2. $6.24\text{N}$
3. $2.68\text{N}$
4. $4.34\text{N}$

Q. $n$ blocks of different masses are placed on a frictionless inclined plane such that they are just in contact with each other. If they are released simultaneously, then find the force of interaction between $(n-1{)}^{th}$ block and $n^{th}$ block

1. $(m_{n-1}-m_n)g\sin \theta$
2. zero
3. $mng\cos \theta$
4. None of these

Q. Block $A$ of mass $m$ placed on a smooth inclined plane is connected by a string to another block $B$ of mass $M$ as shown in the figure. If the system is in equilibrium , express $M$ in terms of $m$

1. $m\sin \theta$
2. $m\cos \theta$
3. $2m\sin \theta$
4. $2m\cos \theta$

Q. The contact force between $2\text{kg}$ and $3\text{kg}$ block placed on an inclined plane as shown in the figure will be

1. $3\text{N}$
2. $6\text{N}$
3. $12\text{N}$
4. $18\text{N}$

Q. Three blocks are placed on a smooth inclined plane with force acting on $m_1$ parallel to the inclined plane. Find the contact force between $m_2$ and $m_3$.

1. $\frac{(m_1+m_2+m_3)F}{m_3}$
2. $\frac{m_{3}F}{m_1+m_2+m_3}$
3. $F-(m_1+m_2)g$
4. None of these

Q. Three blocks of mass $10\text{kg}$, $5\text{kg}$ and $8\text{kg}$ are connected to each other with a light string and placed on a wedge with angle of inclination ${30}^{\circ }$. A force F applied on the string causes all the three blocks to move with a common acceleration of $2m/s^2$. If the coefficient of friction between the blocks and the surface of the wedge is $0.2$, then what is the tension at the three points $A,B$ and $C$?

1. $T_A=200.8N,T_B=69.85N,T_C=113.51N$
2. $T_A=113.51N,T_B=69.85N,T_C=200.8N$
3. $T_A=200.8N,T_B=113.51N,T_C=69.85N$
4. $T_A=195N,T_B=60N,T_C=100N$

Q. Block $A$ of mass $m$ placed on a smooth inclined plane is connected by a string to another block $B$ of mass $M$ as shown in the figure. If the system is in equilibrium , express $M$ in terms of $m$

1. $m\sin \theta$
2. $m\cos \theta$
3. $2m\sin \theta$
4. $2m\cos \theta$

Q. In the figure shown, both the blocks are of equal mass of $10kg$ and $F=300N$. Find the value of tension $T$ in the string in between the blocks.

1. $100N$
2. $150N$
3. $200N$
4. $250N$

Q. In the figure shown, both the blocks are of equal mass of $10kg$ and $F=300N$. Find the value of tension $T$ in the string in between the blocks.

1. $100N$
2. $150N$
3. $200N$
4. $250N$

Q. In the given figure, what maximum force F can be applied on wedge of mass M, so that block of mass m does not move with respect to wedge.

1. 
   $\frac{(M+m)(sin\theta +\mu cos\theta )g}{(cos\theta -\mu sin\theta )}$
2. 
   $\frac{(M+m)(cos\theta +\mu sin\theta )g}{(sin\theta -\mu cos\theta )}$
3. 
   $\frac{(M+m)(sin\theta -\mu cos\theta )g}{(cos\theta +\mu sin\theta )}$
4. 
   $\frac{(M+m)(sin\theta +\mu cos\theta )g}{(sin\theta +\mu cos\theta )}$

Q. Three blocks of mass $10\text{kg}$, $5\text{kg}$ and $8\text{kg}$ are connected to each other with a light string and placed on a wedge with angle of inclination ${30}^{\circ }$. A force F applied on the string causes all the three blocks to move with a common acceleration of $2m/s^2$. If the coefficient of friction between the blocks and the surface of the wedge is $0.2$, then what is the tension at the three points $A,B$ and $C$?

1. $T_A=200.8N,T_B=69.85N,T_C=113.51N$
2. $T_A=113.51N,T_B=69.85N,T_C=200.8N$
3. $T_A=200.8N,T_B=113.51N,T_C=69.85N$
4. $T_A=195N,T_B=60N,T_C=100N$

Q. Find the height by which the sphere rises when the wedge moves and touches the wall. The distance between the wedge and the wall is $10\text{m}$ and the wedge is moved to the left until it touches the wall. Answer in metre.
Take $\sqrt{3}=1.73$

Q. Two blocks are connected over a massless pulley as shown in the figure. The mass of block $A$ is $10\text{kg}$. If block $A$ slides down the inclined plane at constant speed, then mass of block $B$ in $\text{kg}$ is

1. $4$
2. $3$
3. $2$
4. $5$

Q. Which will have the highest speed when it reaches the bottom of the incline?

1. 1
2. 2
3. 3
4. All 3 will have the same speed

Q. A block of mass $m$ is kept on an inclined plane of a lift moving down with acceleration of $2{\text{m/s}}^2$. What should be the coefficient of friction for the block to move down with constant velocity relative to lift?

1. $\mu =\frac{1}{\sqrt{3}}$
2. $\mu =0.4$
3. $\mu =0.8$
4. $\mu =0.5$

Q. By what distance do the wedges move if horizontal plank moves by $x\text{cm}$ downwards?

1. $x\tan \theta \text{cm}$
2. $x\cot \theta \text{cm}$
3. $x\sin \theta \text{cm}$
4. $x\cos \theta \text{cm}$

Q. A block of mass $m$ is in equilibrium on an inclined plane as shown.


Find out the normal force acting on the block

1. $\frac{2mg}{\sqrt{3}}$
2. $\frac{4mg}{\sqrt{3}}$
3. $\frac{\sqrt{3}mg}{4}$
4. $\frac{mg}{2\sqrt{3}}$

Q. In the figure shown, find the velocity acquired by the block on reaching the ground and the force exerted by the inclined plane on the block if takes 5 seconds for the block to reach the ground. Assume all surfaces to be smooth. (Take $g=10m/s^2)$

1. $10m/s,10\sqrt{3}N$
2. $20m/s,10N$
3. $25m/s,20N$
4. $25m/s,10\sqrt{3}N$

Q. What is the acceleration of the block?

1. $g$
2. $gcos\theta$
3. $gsin\theta$
4. $gtan\theta$