Net Acceleration for Non Uniform Circular Motion

Q.

What work is done by a body moving along a circular path? Explain.

Q.

A body is whirling a stone tied with a string in a horizontal circular path. The string breaks, the stone:

1. will continue to move in the circular path

2. will move along a straight line towards the centre of the circular path.

3. will move along a straight line tangential to the circular path.

4. will move along a straight line perpendicular to the circular path away from the boy.

Q. A particle moves in a circular path of radius $R$ with an angular velocity $\omega =a-bt$, where $a$ and $b$ are positive constants and $t$ is time. The magnitude of the acceleration of the particle after time $\frac{2a}{b}$ is

1. $\frac{a}{R}$
2. $a^{2}R$
3. $R\sqrt{a^4+b^2}$
4. none of these

Q. A particle of mass $10\text{g}$ moves along a circle of radius $6.4\text{cm}$ with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle is equal to $8\times {10}^{-4}\text{J}$, by the end of the second revolution (after the beginning of the motion)?

1. $0.15{\text{m/s}}^2$
2. $0.18{\text{m/s}}^2$
3. $0.2{\text{m/s}}^2$
4. $0.1{\text{m/s}}^2$

Q.

Diagram shows the direction of the total acceleration and velocity of a particle moving clockwise in a circle of radius 5/√3 m at an instant of time. Tangential acceleration at this instant is 5 m/s². Which of the following statements is not correct?

1. The centripetal acceleration is $5\sqrt{3}$$m/s^2$

2. Particle is speeding up

3. The net acceleration is 10 $m/s^2$

4. The particle is slowing down

Q.

The coefficient of friction between the tyres and the road is 0.25. The maximum speed with which a car can be driven round a curve of radius 40 m without skidding is $(assumeg=10m{s}^{-2})$

1. $40m{s}^{-1}$

2. $20m{s}^{-1}$

3. $15m{s}^{-1}$

4. $10m{s}^{-1}$

Q. A body moves in a circle of radius $1m$. Its speed is given by $v=2t^2$. FInd the net acceleration at $t=2$ seconds.

1. $\sqrt{1616}m/s^2$
2. $\sqrt{3240}m/s^2$
3. $\sqrt{3814}m/s^2$
4. $\sqrt{4160}m/s^2$

Q.

A motor cycle driver doubles its velocity when he is having a turn. The force exerted outwardly will be

1. Double

2. Half

3. 4 times

4. $\frac{1}{4}times$

Q.

A road is 10 m wide. Its radius of curvature is 50 m. The outer edge is above the lower edge by a distance of 1.5 m. This road is most suited for the velocity

1. 2.5 m/sec

2. 4.5 m/sec

3. 6.5 m/sec

4. 8.5 m/sec

Q. A particle starts from rest, travelling on a circle with constant tangential acceleration. The angle between velocity vector and acceleration vector, at the moment when the particle completes half the circular track is

1. ${\tan }^{-1}\left(2\pi \right)$
2. ${\tan }^{-1}\left(\pi \right)$
3. ${\tan }^{-1}\left(3\pi \right)$
4. ${\tan }^{-1}\left(2\right)$

Q.

Diagram shows the direction of the total acceleration and velocity of a particle moving clockwise in a circle of radius 5/√3 m at an instant of time. Tangential acceleration at this instant is 5 m/s². Which of the following statements is not correct?

1. The centripetal acceleration is $5\sqrt{3}$$m/s^2$

2. Particle is speeding up

3. The net acceleration is 10 $m/s^2$

4. The particle is slowing down

Q. A body is moving with a constant speed of $5\text{m/s}$ in a circle of radius $2\text{m}$. The net acceleration of the body is

1. $0$
2. $12.5{\text{ms}}^{-2}$
3. $25{\text{ms}}^{-2}$
4. None of these

Q. Certain neutron stars are believed to be rotating at about 1 rec/sec. If such a star has a radius of 20 km, the acceleration of an object on the equator of the star will be

1. $20\times {10}^{8}m/se{c}^2$
2. $8\times {10}^{5}m/se{c}^2$
3. $120\times {10}^{5}m/se{c}^2$
4. $4\times {10}^{8}m/se{c}^2$

Q. Tangential acceleration of a particle moving in a circle of radius $1\text{m}$ varies with time $t$ as shown in the figure (initial velocity of particle is zero). Time after which total acceleration of particle makes an angle of ${30}^{\circ }$ with radial acceleration is

1. $4\text{s}$
2. $4/3\text{s}$
3. $2^{2/3}\text{s}$
4. $\sqrt{2}\text{s}$

Q. A car is moving along a circular path of radius $500m$ with a speed of $30m/s$. If at some instant, its speed increases at the rate of $2m/s^2$, then at that instant, the magnitude of resultant acceleration will be

1. $4.7m/s^2$
2. $3.8m/s^2$
3. $3m/s^2$
4. $2.7m/s^2$

Q. A car is moving along a circular path of radius $500m$ with a speed of $30m/s$. If at some instant, its speed increases at the rate of $2m/s^2$, then at that instant, the magnitude of resultant acceleration will be

1. $4.7m/s^2$
2. $3.8m/s^2$
3. $3m/s^2$
4. $2.7m/s^2$

Q. The total acceleration of a particle in circular motion is $25m{s}^{-2}.$ If the speed of the particle decreases at a rate of $15m{s}^{-2}.$ If radius of the path of the particle is $r=2m$, the angular speed $\omega$ of the particle relative to the centre of the circle is

1. $1\frac{rad}{s}$
2. $\sqrt{10}\frac{rad}{s}$
3. $2\frac{rad}{s}$
4. $2\sqrt{10}\frac{rad}{s}$

Q. A particle of mass $10\text{g}$ moves along a circle of radius $6.4\text{cm}$ with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle is equal to $8\times {10}^{-4}\text{J}$, by the end of the second revolution (after the beginning of the motion)?

1. $0.15{\text{m/s}}^2$
2. $0.18{\text{m/s}}^2$
3. $0.2{\text{m/s}}^2$
4. $0.1{\text{m/s}}^2$

Q. For a particle moving along a circle of radius $8m$, the time dependent tangential acceleration is given by $a_t=k{t}^{2}m/s^2$ . Initially, if the particle is at rest and the total acceleration of the particle makes ${45}^{\circ }$ with the tangential acceleration after 2 sec, the value of $k$ (in $m/s^4$ is

Q. In the given figure , $a=10\sqrt{2}{\text{m/s}}^2$ represents the total acceleration of a particle moving in the clockwise direction on a circle of radius $R=2\text{m}$ at a given instant of time. Speed of the particle is:

1. $2\sqrt{5}\text{m/s}$
2. $3\sqrt{5}\text{m/s}$
3. $5\sqrt{2}\text{m/s}$
4. $5\sqrt{3}\text{m/s}$

Q.

A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of 'P' is such that it sweeps out a length $s=t^3+5$, where s is in meters and t is in seconds. The radius of the path is 20 m. The acceleration of 'P' when t = 2 s is nearly

1. 13 m/s²

2. 12 m/s²

3. 7.2 m/s²

4. 14 m/s²

Q. A scooterist is approaching a circular turn of radius $80\text{m}$. He reduced his speed from $27{\text{kmh}}^{-1}$ at constant rate of ${\text{0.5 ms}}^{-2}$. Find net acceleration and angle made by it wrt tangential deceleration

1. ${\text{0.86 ms}}^{-2},{54}^{\circ }$
2. ${\text{0.68 ms}}^{-2},{45}^{\circ }$
3. ${\text{1.0 ms}}^{-2},{45}^{\circ }$
4. ${\text{0.5 ms}}^{-2},{45}^{\circ }$

Q. In the given figure , $a=10\sqrt{2}{\text{m/s}}^2$ represents the total acceleration of a particle moving in the clockwise direction on a circle of radius $R=2\text{m}$ at a given instant of time. Speed of the particle is:

1. $2\sqrt{5}\text{m/s}$
2. $3\sqrt{5}\text{m/s}$
3. $5\sqrt{2}\text{m/s}$
4. $5\sqrt{3}\text{m/s}$

Q.

An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 r.p.m. The acceleration of a point on the tip of the blade is about

1. $1600m/se{c}^2$

2. $4740m/se{c}^2$

3. $2370m/se{c}^2$

4. $5055m/se{c}^2$

Q. Let $a_r$ and $a_t$ represent radial and tangential accelerations. The motion of a particle may be circular, if

1. $a_r=0,a_t=0$
2. $a_r=0,a_t\ne 0$
3. $a_r\ne 0,a_t=0$
4. None of these

Q. A body moves in a circle of radius $1\text{m}$. Its speed is given by $v=2t^2$. Find the net acceleration at $t=2\text{s}$

1. $\sqrt{1616}{\text{m/s}}^2$
2. $\sqrt{3240}{\text{m/s}}^2$
3. $\sqrt{3814}{\text{m/s}}^2$
4. $\sqrt{4160}{\text{m/s}}^2$

Q. A particle is moving with speed $v=2t^2$ on the circumference of a circle of radius $R$. Match the quantities given in Table-1 with corresponding results in Table-2.

Table-1	Table-2
(A) Magnitude of tangential acceleration of particle	(P) decreases with time
(B) Magnitude of centripetal acceleration of particle	(Q) increases with time
(C) Magnitude of angular speed of particle with respect to centre of circle	(R) remains constant
(D) Angle between the total acceleration and centripetal acceleration of particle	(S) depends on the value of radius

1. (A) - Q; (B) - Q; (C) - Q; (D) - P, S
2. (A) - Q; (B) - Q, S; (C) - Q, S; (D) - P, S
3. (A) - Q; (B) - Q, S; (C) - Q, S; (D) - P
4. (A) - Q; (B) - P, S; (C) - P, S; (D) - Q, S