Friction: Bottom Most Point

Q. A cubical block of side $L$ rests on a rough horizontal surface with coefficient of friction $\mu$. A horizontal force $F$ is applied on the block as shown in figure. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is

1. infinitesimal
2. $\frac{mg}{4}$
3. $\frac{mg}{2}$
4. $mg(1-\mu )$

Q. As shown in figure, a uniform disc of mass $m$ is rolling without slipping with an angular velocity $\omega$. The portion $AB$ is rough and $BC$ is smooth. If the disc crosses point $B$, the motion of the disc will be:

1. translational motion only
2. pure rolling motion
3. rotational motion only
4. none of these

Q. A uniform ladder of mass $10\text{kg}$ leans against a smooth vertcal wall making an angle ${53}^{\circ }$ with it. The other end rests on a rough horizontal floor. Then, the friction coefficient just necessary for the ladder to be at rest is approximately

Q. A rigid body of mass $m$ and radius $R$ rolls without slipping on a rough surface. A force is acting on the rigid body at distance $x$ from the centre as shown in figure. Find the value of $x$ so that static friction will be zero.

1. $\frac{I_{\text{cm}}}{2mR}$
2. $\frac{2I_{\text{cm}}}{mR}$
3. $\frac{I_{\text{cm}}}{mR}$
4. $\frac{2I_{\text{cm}}}{3mR}$

Q. When a body rolls without sliding, up an inclined plane, the frictional force is

1. Directed up the plane

2. directed down the plane

3. zero

4. dependent on its velocity

Q. A body of mass $m$ and radius $R$ is rotating with angular velocity $\omega$ as shown in figure and kept on a surface that has sufficient friction. Then, the body will move:

1. initially in backward direction, then along forward direction
2. initially in forward direction, then along backward direction
3. none of these
4. will always move along forward direction.

Q. A disc of mass $m$ and radius $R$ is placed over a plank of same mass $m$. There is sufficient friction between disc and plank to prevent slipping. A force $F$ is applied at the centre of the disc. Which option(s) is/are correct.
[$a=$ acceleration of disc and $f=$ force of friction]

1. $a=\frac{F}{2M}$
2. $a=\frac{2F}{3M}$
3. $f=\frac{F}{3}$
4. $f=\frac{2F}{3}$

Q.
Consider a uniform cubical box of side ${}^{\prime }{a}^{\prime }$ on a rough floor that is to be moved by applying minimum possible force F at a point ${}^{\prime }{b}^{\prime }$ above its centre of mass (see figure). If the coefficient of friction is $\mu =0.4,$ the maximum possible value of $100\times \frac{b}{a}$ for the box not to topple before moving is .

Q. As shown in figure, a uniform disc of mass $m$ is rolling without slipping with an angular velocity $\omega$. The portion $AB$ is rough and $BC$ is smooth. If the disc crosses point $B$, the motion of the disc will be:

1. translational motion only
2. pure rolling motion
3. rotational motion only
4. none of these

Q. A body of mass $m$ and radius $R$ is rotating with angular velocity $\omega$ as shown in figure and kept on a surface that has sufficient friction. Then, the body will move:

1. initially in backward direction, then along forward direction
2. initially in forward direction, then along backward direction
3. will always move along forward direction.
4. none of these

Q. Assertion :A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling motion) Reason: For perfect rolling motion, work done against friction is zero.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. In the projectile motion , if air resistance is ignored , the horizontal motion is at

1. variable acceleration
2. constant acceleration
3. constant velocity
4. constant retardation

Q. The maximum frictional force that comes into play when a body just begins to slide over the surface of another body is known as:

1. Dynamic friction
2. Kinetic friction
3. Rolling friction
4. Limiting friction

Q. Statement 1: A wheel moving down frictionless inclined plane will slip and not roll on the plane.
Statement 2: It is the frictional force which provides a torque necessary for a body to roll on a surface.

1. Statement 1 is false, Statement 2 is true
2. Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1
3. Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1
4. Statement 1 is true, Statement 2 is false

Q. Assertion :A solid sphere is rolling on a rough horizontal surface. Acceleration of contact point is zero. Reason: A solid sphere can roll on the smooth surface.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q.

What is damped SHM ?

Q. In the arrangement, the minimum value of tension in the string to prevent it from sliding down is :

1. $8N$
2. $6N$
3. $10.8N$
4. Zero

Q. A ball of mass moving with constant velocity $u$ collides with a smoooth horizontal surface at $O$ as show in figure. Neglect gravity and friction. The y-axis is drawn normal to the horizontal surface at the point of impact $O$ and x-axis is horizontal as shown. About which point will the angular momentum of ball be conserved?

1. Point B
2. Point A
3. Point C
4. None of these

Q. A round shaped body is released on an inclined plane. Friction is sufficient for pure rolling, mass of body is m & it is released from a height "h". Then which of the following is correct?

1. Work done by friction is negative
2. At bottom total weight is less than mgh
3. Total K.E. on the ground is mgh & ratio of $K{E}_{trans}$ & $K{E}_{rotative}$ depends upon shape of the body
4. None of the above

Q. A rolling body is kept on a plank B. There is sufficient friction between A and B and no friction between B and the inclined plane. Then body

1. A rolls
2. A does not experience any friction
3. A and B has equal acceleration and unequal velocities
4. A rolls depending upon the angle of inclination $\theta$

Q. A body is moving on a rough horizontal table in a circular path being tied to a nail by a string. While the body is in motion, match the quantities in column-I with their description in column-II.
Column-I Column-II

Q. Assertion :In a plane projectile motion, the angle between instantaneous velocity vector and acceleration vector can be anything between $0$ or $\pi$ (excluding the limiting case). Reason: In plane to plane projectile motion, acceleration vector is always pointing vertical downwards. (neglect air friction).

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q. Consider the following two statements A and B, and identify the correct choice in the given answer
A. For a body resting on a rough horizontal table, it is easier to pull at an angle than push at the same angle to cause motion.
B. A body sliding down a rough inclined plane of inclination equal to angle of friction has non-zero acceleration.

1. Both A & B are true
2. Both A & B are false
3. A is false but B is true
4. A is true but B is false

Q. A ball is given a velocity $v$ and angular velocity such that the ball rolls purely on a plank whose upper surface is rough enough to prevent slipping but lower surface in contact with the ground is smooth. No other force is acting on system.

1. The plank will also move forward but with a lesser velocity than that of the ball.
2. The plank will recoil back.
3. The plank will also move forward but with a greater velocity that that of the ball.
4. The plank will remain at rest.

Q. As shown in figure, a uniform disc of mass $m$ is rolling without slipping with an angular velocity $\omega$. The portion $AB$ is rough and $BC$ is smooth. If the disc crosses point $B$, the motion of the disc will be:

1. translational motion only
2. pure rolling motion
3. rotational motion only
4. none of these

Q. When a body rolls without sliding, up an inclined plane, the frictional force is

1. Directed up the plane
2. Directed down the plane
3. Zero
4. Dependent on its velocity

Q. Assertion :Two identical solid balls, one of ivory and the other of wet-clay are dropped from the same height on the floor. Both the balls will rise to same height after bouncing. Reason: Ivory and wet-clay have same elasticity.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. A wedge is moving rightwards on which a block of mass 10kg is placed on it. Friction coefficient between the wedge and the block is 0.8. $[takeg=10m/s^2]$. Select correct alternative(s) among the following options.

1. If wedge is moving with constant velocity then friction acting on block is 64N.
2. If wedge is moving with constant velocity then acceleration of block is zero.
3. If wedge is moving with $\overrightarrow{a}=2\left(\hat{i}\right)m/s^2$ then friction acting on block is 44N.
4. If wedge is moving with $\overrightarrow{a}=10\left(\hat{i}\right)m/s^2$ then friction is 20N.

Q. A wedge moving rightwards has a block of mass 10 kg placed on it. The coefficient of friction between the wedge and the block is 0.8. [take $g=10m{s}^{-2}$]. Select the correct alternative(s) from the following options:

1. If wedge is moving with constant velocity, then friction acting on the block is 64 N.
2. If wedge is moving with $a=2\left(\hat{i}\right)m/s^2$, then friction acting on the block is 44 N.
3. If wedge is moving with $a=10\left(\hat{i}\right)m/s^2$, then friction is 20 N, downward on the wedge along the inclined.
4. If wedge is moving with constant velocity, then acceleration of the block is zero.

Q. Considering a body of mass $m$, radius $R$ rotating with angular speed $\omega$ about the centre of mass and with a velocity $v$ of centre of mass, the most appropriate definition of rolling motion will be

1. $v=R\omega$
2. The point of contact is stationary
3. The point of contact is stationary with respect to the surface
4. The body purely rotates about the point of contact.