Friction and Vertical Circular Motion Problems

Q.

What is the distance between two protons if the electrical repulsive force between them is equal to the weight of either proton

1. 0.102 m

2. 0.103 m

3. 0.011 m

4. 0.118 m

Q. An electric dipole of length $4\text{cm}$ , when placed with its axis making an angle of ${60}^{\circ }$ with a uniform electric field , experiences a torque of $4\sqrt{3}\text{Nm}$. Find the potential energy of the dipole, if the dipole has charges of $\pm 8\text{nC}$ (in $\text{J}$)

1. $-2\text{J}$
2. $+2\text{J}$
3. $+4\text{J}$
4. $-4\text{J}$

Q. An electric dipole of length $2\text{cm}$ is placed with its axis making an angle of ${30}^{\circ }$ to a uniform electric field having intensity ${10}^5\text{N/C}$. If it experiences a torque of $10\sqrt{3}\text{N-m}$, then the potential energy of the dipole is

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

Q. An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency $\omega$ will be -

1. $2\sqrt{\frac{qE}{md}}$
2. $\sqrt{\frac{qE}{md}}$
3. $\sqrt{\frac{qE}{2md}}$
4. $\sqrt{\frac{2qE}{md}}$

Q.

How is angular frequency different from angular velocity?

Q. A tank is filled with a liquid upto a height H. A small hole is made at the bottom of this tank. Let $t_1$ be the time taken to empty first half of tank and $t_2$ the time taken to empty rest half of the tank. Then find $\frac{t_1}{t_2}$ (assume non viscous and in compressible fluid flowing in stream line manner)

1. 0.414
2. 0.212
3. 0.313
4. 0.515

Q. A mass $m$ attached to a thin wire is whirled in a vertical circle with a constant speed. The wire is most likely to break when

1. the mass is at the highest point.
2. the wire is horizontal.
3. the mass is at the lowest point.
4. inclined at an angle of $60°$ from vertical.

Q. A body is allowed to slide on a frictionless track from rest position under gravity. The track ends into a circular loop of diameter $D$. What should be the minimum height of the body in terms of $D$ so that it may complete the loop successfully?

1. $\frac{4}{5}D$
2. $\frac{5}{4}D$
3. $1D$
4. $2D$

Q. A particle of mass $m$ begins to slide down a fixed smooth sphere from the top as shown. What is its acceleration when it breaks off the sphere?

1. $2g/3$
2. $g/3$
3. $g$
4. $\sqrt{5}g/3$

Q.

A metal sphere of radius 1 mm and mass 50 mg falls verticcally in glycerine. Find (a) the viscous force exerted by the glycerine on the sphere when the speed of the sphere is 1 cm s^{-1}, (b) the hydrostatic force exerted by the glycerine on the sphere and (c) the terminal velocity with which the sphere will move down without acceleration. Density of glycerine = $1260kg{m}^{-3}$ and its coefficient of viscosity at room temperature = 8.0 poise.

Q. An electric dipole of length $2\text{cm}$ is placed with its axis making an angle of ${30}^{\circ }$ to a uniform electric field ${10}^5\text{N/C}$.If it experiences a torque $10\sqrt{3}\text{Nm}$, then potential energy of the dipole

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

Q.

What affects the period of oscillation

Q.

As shown in the figure, a particle of mass $10kg$ is placed at point $A$. When the particle is slightly displaced to its right, it starts moving and reaches point $B$. The speed of the particle at $B$ is $xm{s}^{-1}$. (Take $g=10m{s}^{-1}$ ) The value of $x$to the nearest integer is $\_\_\_\_\_\_\_.$

Q. A piece of wire is bent in the shape of a parabola $y=k{x}^2$ (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stays at rest with respect to the wire, from the y-axis is

1. $\frac{a}{gk}$
2. $\frac{a}{2gk}$
3. $\frac{2a}{gk}$
4. $\frac{a}{4gk}$

Q. A rod of mass M and length 2L is performing SHM as Torsional pendulum in horizontal plane. Two blocks each of mass m are put at distance $\frac{L}{2}$ from centre. The frequency after putting blocks of mass m is 20% of initial frequency. Then ratio of $\frac{m}{M}$ will be :

1. 12
2. 14
3. 16
4. 18

Q.

suppose the rod with the balls A and B of the previous problem is clamped at the centre in such a way that it can rotate freely about a horizontal axis through the clamp. The system is kept at rest in the horizontal position. A particle P of the same mass m is dropped from a height h on the ball B. The particle collides with B and sticks to it. (a) Find the angular momentum and the angular speed of the system just after the collision. (b) What should be the minimum value of h so that the system makes a full rotation after the collision.

Q.

Does a pendulum swing faster with more weight$?$

Q. A horizontal wire carries 200A current below which another wire of linear density $20\times {10}^{-3}kg/m$ carrying a current is kept at 2 cm distance. If the wire kept below hangs in air, then the current in the wire is

1. 9.8 A
2. 9800A
3. 980 A
4. 98 A

Q. A bob attached to a light string is rotating in a vertical circle of radius $5\text{m}$. If the velocity of the bob at its lowest point is twice the velocity of the bob when it makes an angle of ${90}^0$ with the vertical. Will the bob complete a full circle? If yes, what is the velocity of the bob at its highest point?

1. The bob will not complete the full circle.
2. The bob will complete the circle and the velocity at the highest point will be $9.12\text{m/s}$.
3. The bob will complete the circle and the velocity at the highest point will be $5.77\text{m/s}$.
4. The bob will complete the circle and the velocity at the highest point will be $7.87\text{m/s}$.

Q.

Three identical cars A, B and C are moving at the same speed on three bridges. The car A goes on a plane bridge, B on a bridge convex upward and C goes on a bridge concave upward. Let $F_A,F_{B}and{F}_C$ be the normal forces exerted by the cars on the bridges when they are at the middle of bridges.

1. is maximum of the three forces.

2. = =

3. is maximum of the three forces.

4. is maximum of the three forces.

Q.

A pendulum having time period equal to two seconds is called a seconds pendulum. Those used in pendulum clocks are of this type. Find the length of a seconds pendulum at a place where $g={\pi }^{2}m{s}^{-2}.$

Q.

A body is attached to the lower end of a vertical spiral spring and it is gradually lowered to its equilibrium position. This stretches the spring by a length x. If the same body attached to the same spring is allowed to fall suddenly, what would be the maximum stretching in this case

1. 

2. 

3. 

4. 

Q. A boat of length $10\text{m}$ and mass $450\text{kg}$ is floating without motion in still water. A man of mass $50\text{kg}$ standing at one end of it walks to the other end of it and stops. The magnitude of the displacement of the boat (in $\text{metre}$) relative to ground is

1. $0$
2. $1$
3. $2$
4. $5$

Q.

Two small metal balls of different mass $m_{1}and{m}_2$ are connected by strings of equal length to a fixed point. When the balls are given charges, the angles that the two strings make with the vertical are ${30}^{\circ }and{60}^{\circ }$, respectively. The ratio $m_1/m_2$ is close to

1. 1.7

2. 3.0

3. 0.58

4. 2.0

Q.

. Which of the following has the least value of coefficient of friction?

1. Rolling friction

2. Limiting friction

3. Static friction

4. Sliding friction

Q.

A 1 kg stone at the end of 1 m long string is whirled in a vertical circle at constant speed of 4 m/sec. The tension in the string is 6 N, when the stone is at (g = 10 m/$se{c}^2$)

1. None of the above

2. Bottom of the circle

3. Top of the circle

4. Half way down

Q. The angular displacement of a simple pendulum is given by $\theta =\frac{\pi }{20}cos(\omega t+\frac{\pi }{6})$ (in radians), where $\omega =2rad/s$. Find length of pendulum.

1. 2.50 m
2. 1.60 m
3. 1.44 m
4. 6.25 m

Q.

A one metre long stretched string having a mass of 40 g is attached to a tuning fork. The fork vibrates at 128 Hz in a direction perpendicular to the string. What should be the tension in the string if it is to vibrate in four loops ?

Q.

Does weight affect the speed of a pendulum?

Q. A string attached to a light thread is whirled in a vertical circle with a constant velocity $v$. The radius of the circle is $10\text{m}$. The maximum and minimum tension of the string is in the ratio $4:1$. What is the value of velocity $v$?
(Take $g=10{\text{m/s}}^2$)

1. $15.1\text{m/s}$
2. $12.9\text{m/s}$
3. $13.5\text{m/s}$
4. $10.9\text{m/s}$