Net Acceleration for Non Uniform Circular Motion

Q.

What is meant by positive work, negative work, and zero work? Illustrate your answer with an example?

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

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

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

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

Q. A particle moves in a circle of radius $25cm$ at two revolutions per second. The acceleration of the particle in $m/s^2$ is

1. ${\pi }^2$
2. $8{\pi }^2$
3. $4{\pi }^2$
4. $2{\pi }^2$

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 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. 4.5 m/sec

2. 2.5 m/sec

3. 6.5 m/sec

4. 8.5 m/sec

Q. A stone tied to the end of a string $80\text{cm}$ long is whirled in a horizontal circle with a constant speed. If the stone makes $14$ revolutions in $25\text{sec}$, then magnitude of acceleration of the same will be

1. $990{\text{cm /sec}}^2$
2. $680{\text{cm /sec}}^2$
3. $650{\text{cm /sec}}^2$
4. $750{\text{cm /sec}}^2$

Q. A small object moves counter clockwise along the circular path whose centre is at the origin as shown in figure. As it moves along the path, its net acceleration vector continuously points towards point $\text{S}$. Then the object

1. Speeds up as it moves from $\text{A}$ to $\text{C}$ via $\text{B}$.
2. Slows down as it moves from $\text{A}$ to $\text{C}$ via $\text{B}$.
3. Slows down as it moves from $\text{C}$ to $\text{A}$ via $\text{D}$.
4. Speeds up as it moves from $\text{C}$ to $\text{A}$ via $\text{D}$.

Q.

Raw and boiled eggs are made to spin on a smooth table by applying the same torque. The egg that spin faster is

1. Raw egg

2. Boiled egg

3. Both will have same spin rate

4. Difficult to predict

Q.

A mass of 100 gm is tied to one end of a string 2 m long. The body is revolving in a horizontal circle making a maximum of 200 revolutions per min. The other end of the string is fixed at the centre of the circle of revolution. The maximum tension that the string can bear is (approximately)

1. 89.42 N

2. 87.64 N

3. 8.76 N

4. 8.94 N

Q.

The maximum velocity (in $m{s}^{–1}$) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is

1. 25

2. 60

3. 30

4. 15

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 particle is moving on a circular path with constant speed, then its acceleration will be

1. Constant acceleration

2. External radial acceleration

3. Zero

4. Internal radial acceleration

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.

A stone tied to a string is rotated in a circle. If the string is cut, the stone flies away from the circle because

1. A centrifugal force acts on the stone

2. A centripetal force acts on the stone

3. Of its inertia

4. Reaction of the centripetal force

Q. A block rests on a horizontal table which is executing an SHM in the horizontal plane with an amplitude a. If the coefficient of friction is m, the block just starts to slip when the frequency of oscillation is:

1. $\sqrt{\frac{\mu g}{a}}$
2. $2\pi \sqrt{\frac{\mu g}{a}}$
3. $\frac{1}{2\pi }\sqrt{\frac{a}{\mu g}}$
4. $\frac{1}{2\pi }\sqrt{\frac{\mu g}{a}}$

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. For a particle moving along circular path, the radial acceleration $a_r$ is proportional to time $t$. If $a_t$ is the tangential acceleration, then which of the following will be independent of time?

1. $a_t$
2. $a_r.a_t$
3. $\frac{a_r}{a_t}$
4. $a_r(a_t{)}^2$

Q. A balloon starts rising from the surface of the earth. The ascension rate is constant and equal to $V_0$. Due to the wind the balloon gathers a horizontal velocity component $V_x=Ky$ where K is a constant and y is the height of ascent.
The horizontal drift of the balloon depends on the height of the ascent as

1. $\frac{K{y}^2}{V_0}$
2. $\frac{K{y}^2}{2V_0}$
3. $\frac{2K{y}^2}{V_0}$
4. $\frac{K{y}^2}{\sqrt{2}{V}_0}$

Q.

A particle revolves round a circular path. The acceleration of the particle is

1. Along the tangent

2. Along the radius

3. Zero

4. Along the circumference of the circle

Q.

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

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

2. 4 times

3. Double

4. Half

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

Q.

When the displacement is at right angles to the force, work done is _________.

Q. A body is moving in a circle with a speed of $1\text{m/s}$. This speed increases at a constant rate of $2\text{m/s}$ every second. Assume that the radius of the circle described is $25\text{m}$. The total acceleration of the body after $2\text{s}$ is

1. $2{\text{m/s}}^2$
2. $25{\text{m/s}}^2$
3. $\sqrt{7}{\text{m/s}}^2$
4. $\sqrt{5}{\text{m/s}}^2$

Q. A particle is given an initial speed $u$ inside a smooth spherical shell of radius $R=1\text{m}$, so that it is just able to complete the circle. Acceleration of the particle when its velocity is vertical, is

1. $g\sqrt{10}$
2. $g\sqrt{2}$
3. $3g$
4. $g$

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 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. $2.7m/s^2$
4. $3m/s^2$

Q. A car is travelling at $20\text{m/s}$ on a circular road of radius $100\text{m}$ at an instant. If it's speed is increasing at the rate of $3{\text{m/s}}^2,$ it's acceleration (in ${\text{m/s}}^2$) at this instant is-

Q.

Two Circular loops of radius R and nR are made from the same wire . The moment of inertia about the axis passing through centre and perpendicular to the plane of the larger loop is 8 times that of smaller loop. What is value of n

Q. A stone tied to the end of a string $1\text{m}$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolutions in $44$ seconds, what is the magnitude and direction of acceleration of the stone?

1. ${\pi }^2{\text{ms}}^{-2}$ and direction along the radius towards the centre.
2. ${\pi }^2{\text{ms}}^{-2}$ and direction along the radius away from the centre.
3. ${\pi }^2{\text{ms}}^{-2}$ and direction along the tangent to the circle.
4. $\frac{{\pi }^2}{4}{\text{ms}}^{-2}$ and direction along the radius towards the centre.

Q. The total acceleration of a particle in circular motion is $5m/s^2$. If the speed of the particle decreases at a rate of $3m/s^2$, assuming $r=2m$, the angular speed $\omega$ of the particle ( in $rad/s$) relative to the centre of the circle is