Inclined Planes

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. The normal reaction $\text{N}$ for a vehicle of $800\text{kg}$ mass, negotiating a turn on a ${30}^{\circ }$ banked road at maximum possible speed without skidding is _____ $\times {10}^3{\text{kg-m/s}}^2$.

Take $\cos {30}^{\circ }=0.87$ and $\mu =0.2$

1. $10.2$
2. $7.2$
3. $12.4$
4. $6.96$

Q.

What does $9.8\mathrm{N}/\mathrm{kg}$ mean?

Q. Figure shows a wedge of mass $2\text{kg}$ resting on a frictionless floor. A block of mass $1\text{kg}$ is kept on the frictionless wedge and the wedge is given an acceleration of $5{\text{m/s}}^2$ towards right. Then select the correct statement. (Assume $g=10m/s^2$)

1. the block will have an acceleration of $1{\text{m/s}}^2$ w.r.t wedge
2. None of the above
3. the block will remain stationary w.r.t wedge
4. the normal reaction on the block is $11\text{N}$

Q.

An inclined plane makes an angle of ${30}^{\circ }$ with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to $\frac{5g}{n}$, then value of $n$ is

Q. Two blocks $A$ and $B$ of equal masses are released from an inclined plane of inclination ${45}^{\circ }$ at $t=0$ . Both the blocks are initially at rest. The coefficient of kinetic friction between the block $A$ and the inclined plane is $0.2$ while it is $0.3$ for block $B$. Initially the block $A$ is $\sqrt{2}\text{m}$ behind the block $B$. When and where from the position of A, front faces of both the blocks will come in a line? (Take $g=10m/s^2)$

1. $2\text{s},8\sqrt{2}\text{m}$
2. $2\text{s},10\sqrt{2}\text{m}$
3. $1\text{s},10\sqrt{2}\text{m}$
4. $1\text{s},8\sqrt{2}\text{m}$

Q.

Figure shows a rod of length l resting on a wall and the floor. Its lower end A is pulled towards left with a constant velocity u. As a result of this, end B starts moving down along the wall. Find the velocity of the other end B downward when the rod makes an angle $\theta$ with the horizontal.

1. 

2. 

3. 

4. 

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. 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. ntIf a pushing force making an angle alpha with the horizontal is applied on a block of mass m placed on horizontal table and angle of friction is beta, then minimum magnitude. Force required to move block isn ntA)mgsinbeta/cos(alpha-beta)n ntB) mgsinbeta/cos(alpha+beta)n ntC) mgsinbeta/sin(alpha+beta)n ntD)mgcosbeta/cos(alpha-beta)n

Q.

An $80kg$ person is parachuting and is experiencing a downward acceleration of $2.8m{s}^{-2}$. The mass of the parachute is $5kg$. The upward force on the open parachute is (take, $g=9.8m{s}^{-2}$)

1. $595N$

2. $675N$

3. $456N$

4. $925N$

Q.

Transmission delay does not depend on

1. Packet Length

2. Transmission Rate

3. Distance Between The Router

4. Both (A) And (B)

Q. Magnitude of $F$ such that block remains stationary with respect to the wedge. All surfaces are smooth.

1. $2g(M+m)\tan \theta$
2. $g(m-M)\tan \theta$
3. $g(M-m)\tan \theta$
4. $g(M+m)\tan \theta$

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. $\mu =0.8$
3. $\mu =0.4$
4. $\mu =0.5$

Q. A body of mass 1 kg lies on smooth inclined plane. The block of mass m is pushed by a force $F=10\text{N}$ horizontally as shown. The magnitude of net normal reaction on the block is :

1. $10\sqrt{2}\text{N}$
2. None of these
3. $10\text{N}$
4. $\frac{10}{\sqrt{2}}\text{N}$

Q. The mass $M$ of the hanging block in figure which will prevent the small block from slipping over the triangular block, if all the surfaces are frictionless and the strings and the pulleys are light is

1. $\frac{M^{\prime }+m}{\cot \theta -1}$
2. $\frac{M^{\prime }-m}{\cot \theta +1}$
3. $\frac{M^{\prime }+m}{\tan \theta -1}$
4. $\frac{M^{\prime }-m}{\tan \theta +1}$

Q.

What is the value of ‘g’ when a body falls vertically downwards?

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

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

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

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. Block A has a mass of $30\text{kg}$ and block B a mass of $15\text{kg}$. The coefficients of friction between all surfaces of contact are ${\mu }_s=0.15$ and ${\mu }_k=0.10$. Knowing that $\theta ={30}^{\circ }$ and that the magnitude of the force $F$ applied to block A is $250\text{N}$, determine the accelaration of block A.

[Take $g=10{\text{m/s}}^2$]

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

Q. Two blocks of mass $m_1=4\text{kg}$ and $m_2=2\text{kg}$, connected by a weightless rod on a plane having inclination of ${37}^{\circ }$ is shown in figure. If the coefficient of dynamic friction is $\mu =0.25$, then the common acceleration of the two blocks and the tension $\left(T\right)$ in the rod are

1. $2{\text{m/s}}^2,T=5\text{N}$
2. $4{\text{m/s}}^2,T=0\text{N}$
3. $10{\text{m/s}}^2,T=10\text{N}$
4. $15{\text{m/s}}^2,T=9\text{N}$

Q. 21. In an interference pattern the position of zeroth order maxima is 4.8 mm from a certain point on a screen. The frige width is .2 mm the position of 2nd order minima grom point p is?

Q. Two blocks $A$ and $B$ of masses $m_A=1kg$ and $m_B=2kg$ are placed in contact on a frictionless plane of inclination ${30}^{\circ }$. Find the magnitude of contact force between the two blocks when an external force is applied on the blocks as shown in the figure.

1. $2N$
2. $6N$
3. $10N$
4. $12N$

Q. Two blocks $A$ and $B$ of equal masses are released from an inclined plane of inclination ${45}^{\circ }$ at $t=0$ . Both the blocks are initially at rest. The coefficient of kinetic friction between the block $A$ and the inclined plane is $0.2$ while it is $0.3$ for block $B$. Initially the block $A$ is $\sqrt{2}\text{m}$ behind the block $B$. When and where from the position of A, front faces of both the blocks will come in a line? (Take $g=10m/s^2)$

1. $2\text{s},8\sqrt{2}\text{m}$
2. $1\text{s},8\sqrt{2}\text{m}$
3. $2\text{s},10\sqrt{2}\text{m}$
4. $1\text{s},10\sqrt{2}\text{m}$

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

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