Centripetal Acceleration

Q. The pseudo force acting on a particle at rest in a rotating frame of reference is known as

1. centrifugal force
2. centripetal force
3. coriolis force
4. both (a) and (c)

Q.

How is force inversely proportional to distance squared?

Q. The initial velocity of a particle is u (at t = 0) and the acceleration a is given by α t^{3/2}. Which of the following relations is valid?

Q. A plane moving with velocity v turns by theta angle and its speed remains v. Find change in velocity of plane.

Q. The angular velocity of flywheel changes from 240 rpm to 120 rpm in 6 seconds. Calculate the no. of revolutions it will make before coming to rest

Q. A wheel has a speed of 1200 revolutions per minute and is made to slow down at a rate of 4 rad/s^{2 }. The no. of revolutions it makes before coming to rest is how much

Q.

A hollow vertical cylinder of radius R and height h has smooth internal surface. A small particle is placed in contact with the inner side of the upper rim at a point P. It is given a horizontal speed v_o tangential to rim. It leaves the lower rim at point Q, vertically below P. The number of revolutions made by the particle will

1. 

2. 

3. 

4. 

Q. The angle between the radius vector and centripetal acceleration is

1. zero
2. pi/2 radian
3. pi radian
4. none of these

Q.

Which of the following is called a fictitious force?

1. Centripetal force

2. Centrifugal force

3. Frictional force

4. Gravitational force

Q.

A metallic rod of mass 20 kg and of uniform thickness rests against a wall while the lower end of the rod is in contact with floor. The rod makes an angle of ${60}^o$ with floor. If the weight of rod produces a torque 150 Nm about its lower end, the length of the rod is (g = 10$m{s}^{-2}$)

1. 1m

2. 2m

3. 3m

4. 4m

Q. Aprojectile has a range of 50 m and reaches a maximum height of 10 m Calculate the angle which the projectile is firer

Q. A fan of moment of ineria 0.6 kgm^2 is to run upto a working speed of 0.5 revolution per second . Indicate the correct value of the angular moment of fan

Q. what will be the sress at -20^° c, if a steel rod is streched between two fixed points? the tensile load at 20^° c is 5000N (cross sectional area of rod is 150mm^2)

Q. The initial speed of an arrow shot from a bow, at an elevation of 30^°, is 15 ms^{-1}. Find its velocity when it hits the ground back.

Q. What is the SI unit of centrifugal force??

Q.

If the earth stops rotating, the apparent value of g on its surface will

1. Increase everywhere

2. Remain the same everywhere

3. Increase at some places and remain the same at some other places

4. Decrease everywhere

Q. A car is moving with constant speed on a road as shown in figure. The normal reaction by the road on the car is $N_A,N_B$ and $N_C$ when it is at the points A, B and C respectively. Then:

1. $N_A=N_B$
2. $N_A>N_B$
3. $N_A<N_B$
4. $N_A=N_C$

Q.

The instantaneous angular position of a point on a rotating wheel is given by the equation

Θ(t) = 2t³ – 6t²

The torque on the wheel becomes zero at:

1. t=1 s

2. t=2s

3. t=0.5s

4. t=0.25s

Q. Three particles are tied by means of strings of negligible mass and equal lengths. They move on a horizontal circular path of radius ${}^{\prime }{r}^{\prime }$ as shown. Find the tension in the string connecting them.

1. $\frac{mr{\omega }^2}{2-\sqrt{3}}$
2. $\frac{mr{\omega }^2}{2\sqrt{3}}$
3. $\frac{mr{\omega }^2}{2+\sqrt{3}}$
4. $\frac{mr{\omega }^2}{\sqrt{3}}$

Q.

A particle moving along a circular path of radius 5m with constant speed $10\mathrm{m}/\mathrm{s}$. Determine its angular velocity, time period, and acceleration. Also, determine the net force acting on the particle. The mass of the particle is $2\mathrm{kg}.$

Q. A stone is attached at the end of a string and rotated in a horizontal circle by a student. If the final speed of the stone is $2$ times the initial speed, then the final centripetal force is $x$ times the initial centripetal force. The value of $x$ is:

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

Q. A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed ?

Q. A particle moves in a circle of radius 1.0 cm at a speed given by v = 2.0 t where v is cm/s and t in seconds.
(a) Find the radial acceleration of the particle at t = 1 s.
(b) Find the tangential acceleration at t = 1 s.
(c) Find the magnitude of the acceleration at t = 1 s.

Q. An aircraft executes a horizontal loop of radius $1\text{km}$ with a steady speed of $900{\text{kmh}}^{-1}$. Find its centripetal acceleration.

1. $62.5{\text{m/s}}^2$
2. $30{\text{m/s}}^2$
3. $32.5{\text{m/s}}^2$
4. $72.5{\text{m/s}}^2$

Q. An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Compare its centripetal acceleration with the acceleration due to gravity.

Q. The angular acceleration of an rotating body is define by the relation alpha=-k theta . Determine a) the value of k if angular velocity is 8 rad/sec at angular displacement of 0 radian and angular velocity is 0 rad/sec at angular displacement of 4 radian. B) find the angular displacement at angular displacement of 3 radian.

Q. Four particles of equal masses of $1\text{kg}$ are connected by a light inextensible string of equal length to form a square. These are constrained to move along a frictionless ring of radius $2\text{m}$ in horizontal plane with a uniform speed speed of $2\text{m/s}$ as shown in figure. The tension in the string connecting them is

1. $2\sqrt{2}N$
2. $\frac{1}{\sqrt{2}}N$
3. $\sqrt{2}N$
4. $3\sqrt{2}N$

Q. A coin is placed on a turntable which is making $40$ revolutions per minute. The distance of the coin from the center of the turntable is $\frac{3}{{\pi }^2}\text{m}$. The minimum friction coefficient between the turntable and the coin is [Take $g=10{\text{m/s}}^2$]

1. $0.53$
2. $0.72$
3. $0.83$
4. $0.27$

Q. A circular turntable of radius $0.5\text{m}$ has a smooth groove as shown in figure. A ball of mass $90\text{g}$ is placed inside the groove along with a spring of spring constant ${10}^2\text{N/cm}$. The ball is at a distance of $0.1\text{m}$ from the center when the turntable is at rest. On rotating the turntable with a constant angular velocity of ${10}^2\text{rad/sec}$ the ball moves away from the initial position by a distance nearly equal to:

1. $2\times {10}^{-1}\text{m}$
2. ${10}^{-2}\text{m}$
3. ${10}^{-1}\text{m}$
4. ${10}^{-3}\text{m}$

Q. A body is of mass $M$ is kept at rest by means of string connected to a body of mass ${}^{\prime }{m}^{\prime }$ kept on a turn-table rotating with constant angular velocity ${}^{\prime }{\omega }^{\prime }$ as shown. Find the ratio $\frac{M}{m}$. (Neglect the force due to friction)

1. $\frac{g}{l{\omega }^2}$
2. $\frac{l{\omega }^2}{g}$
3. $\sqrt{\frac{l\omega }{g}}$
4. $\frac{2l{\omega }^2}{g}$