20 + Interview Questions in CENTRIPITAL-AND-CENTRIFUGAL-FORCES IN GENERAL AWARENESS Page 1 InterviewSolution

1.	The CG of a loaded truck is at a height of 3 m above the ground and the distance between its wheels is 3m. What is the maximum speed with which it can go round a curved road of radius 200 m without turning turtle ?
Answer» Correct Answer - `31.3 ms^(-1)`

Discussion

2.	Calculate the ratio of the reaction of a convex bridge at the highest point to the reaction of a concave bridge at its lowest point when a car passes at 30 kmph and the radius of either bridge is 20 m.
Answer» Correct Answer - 0.48 : 1

Discussion

3.	A mass of 0.675 kg on a frictionless table is attached to a string which passes through a hole in the table at the centre. If the radius of the circle in which the mass rotates, is 5 m when its speed is `10 ms^(-1)`, find the tension of the string. It is found that on drawing down the string by 0.2 m, the tension is increased 4.63 times. Calculate the work done by the string on the revolving mass during the reduction of the radius. [Hint : Apply work-energy theorem to find work done by the force]
Answer» Correct Answer - `135 N, 60 J`

Discussion

4.	A mass `m` on a frictionless table is attached to a hanging mass M by a cord length `l` passing through a hole in the table. Find the speed with which `m` must spin for M to stay at the highest point. If this speedis doubled, what will be the force with which M will press the table ?
Answer» Correct Answer - `v= sqrt(Mgl//m), 3 Mg`

Discussion

5.	A man stands on a running train (speed 60 kmph) with his feet 60 m apart facing forward. If the train rounds a curve of radius 450 m in a counterclockwise sense, what per cent of his weight rests on his left leg, if his centre of mass is 1.2 m above the floor ?
Answer» Correct Answer - `37.4 %`

Discussion

6.	Calculate the frequency of revolution of an electron in a hydrogen atom assuming that the radius of the first Bohr orbit is `5 xx 10^(-11)`m. Mass of electron `= 9.0 xx 10^(-31) kg` , charge of electron `= 1.6 xx 10^(-19) C, (1)/(4pi epsilon_(0))=9xx10^(9) SI` units.
Answer» Correct Answer - `7.2 xx 10^(15) "rev/sec"`

Discussion

7.	Calculate the apparent weight if a body of 10 kg of place of latitude `60^(@)`. The radius of the earth `= 6.4 xx 10^(6)` m [Hint : Apparent weight `= mg - mv^(2) cos ^(2) lamda/r` where `lamda` is the latitude of the place `= mg - m omega^(2) r cos^(2) lamdaN` `= (m - m omega^(2)r cos^(2) lamda//g)kg`]
Answer» Correct Answer - 9.9914 kg

Discussion

8.	Two particles A and B move anticlockwise with the same speed v in a circle of radius R and are diametrically opposite to each other. At `t=0`, A is given a constant accelerartion (tangential) `a_(t)=(72v^(2))/(25 pi R)`. Calculate the time in which a collides with B, the angle traced by A, its angular velocity and radial acceleration at the time of collision.
Answer» Correct Answer - `t=5pi R//6V, theta = 11 pi//6, a_(t)=289 V^(2)//25 R^(3)`

Discussion

9.	A satellite revolving in a circular equatorial orbit of radius `R = 2xx10^(4)` km from west to east appears over a certain point at the equator every `t = 11.6` hours. Calculate the mass of the earth. The gravitational contant `G= 6.67 xx 10^(-11) SI` units. [Hint : `omega_(app) =omega_("earth") or omega_("real") = 2pi ((1)/(T)+(1)/(t))`]
Answer» Correct Answer - `6 xx 10^(24)` kg

Discussion

10.	A very small cube of mass `m` is placed on the inside of a conial funnelof semivertical angle `(pi//2-theta)`. The funnel is then set in rotation. If the coefficient of static friction between the cube and the funnel is `mu` and the centre of the cube is at a distance`r` from the axis of rotation, what are the largest and smallest angular velocities with which the funnel can be rotated so that the block will not move with respect to the funnel ?
Answer» Correct Answer - `omega_(max)=sqrt((g sin theta+mu cos theta)/(r cos theta-mu sin theta)),omega_(min)=sqrt((g sin theta-mu cos theta)/(rcos theta+mu sin theta))`

Discussion

11.	A body is suspended by a string of length 1 m and is projected horizontally with a velocity of `4 ms^(-1)` Calculate its tangential and radial accelerations when the string rises by `60^(@)` from its initial position.
Answer» Correct Answer - `8.5 ms^(-2),6.2 ms^(-2)`

Discussion

12.	The bob of a simple pendulum of length 1m hangs at rest. It is suddenly projected horizontally with velocity `10 ms^(-1)`. Calculate the velocity of the bob and tension of the string when it is horizontal. The mass of the bob is `(1)/(2)`kg. [Hint : See worked out example 4]
Answer» Correct Answer - `9.87 ms^(-1)`, 40.2 N

Discussion

13.	In problem 17 if the mass `m` is allowed to fall from a height `2R`, find the reaction of the track on the sliding mass the lowest point, at the highest point, at the mid-point. Take `R : r = 5:2`
Answer» Correct Answer - 11 mg, 5 mg, 8 mg

Discussion

14.	A particle of mass m is suspended by a string of length l from a fixed rigid support. Particle is imparted a horizontal velocity `u=sqrt(2gl)`. Find the angle made by the string with the vertical when the acceleration of the particle is inclined to the string by `45^(@)`?
Answer» Correct Answer - `90^(@)`

Discussion

15.	If a simple pendulum of mass `m` is released from a horizontal position, find the tension in the string as a function of the angle `theta` with the horizontal.
Answer» Correct Answer - `T = 3 mg sin theta`

Discussion

16.	In the figure of problem 17 if the block starts from rest when `R = 5r`, what is the reaction of the inner track on the sliding mass at the highest point ? From what height should it fall so that it may exert a force equal to its weight on the track at the highesth point ?
Answer» Correct Answer - 5 mg, 3r

Discussion

17.	A small body is tied to an end of an inextensible string of negligible mass and length r, the other end being clamped to a rigid support. What is the minimum velocity with which the body must be projected horizontally so that it can go completely round a vertical circle without slakening of the string at the highest point ?
Answer» Correct Answer - `sqrt(5gr)`

Discussion

18.	A ring of mass `m` and radius `R` is being rotated about its axis with constant angular velocity `omega` in the gravity free space. Find tension in the ring.
Answer» Correct Answer - `(mw^(2)R)/(2pi)`

Discussion

19.	A mass `m` is moving inside a vertical circular track of radius R. There is no friction. Find the minimum speed `(v_(min))` at which `m` will round the circle without losing contact with the track. Suppose `v = 0.775 v_(min)`. The mass will move up to certain point P where it will lose contact with the track. Find the angular heightr of the track.
Answer» Correct Answer - `sqrt(5)g, sin^(-1) 1//3`

Discussion

20.	A bucket containing water is tied to one end of a rope 2 m long and rotated in a circle about the other end in a vertical plane. Find the minimum number of rotations per minute in order that water may not spill. `(g = 9.8 ms^(-2))`.
Answer» Correct Answer - 21.1

Discussion

Explore topic-wise InterviewSolutions in .

The CG of a loaded truck is at a height of 3 m above the ground and the distance between its wheels is 3m. What is the maximum speed with which it can go round a curved road of radius 200 m without turning turtle ?

Calculate the ratio of the reaction of a convex bridge at the highest point to the reaction of a concave bridge at its lowest point when a car passes at 30 kmph and the radius of either bridge is 20 m.

A mass `m` on a frictionless table is attached to a hanging mass M by a cord length `l` passing through a hole in the table. Find the speed with which `m` must spin for M to stay at the highest point. If this speedis doubled, what will be the force with which M will press the table ?

A man stands on a running train (speed 60 kmph) with his feet 60 m apart facing forward. If the train rounds a curve of radius 450 m in a counterclockwise sense, what per cent of his weight rests on his left leg, if his centre of mass is 1.2 m above the floor ?

Calculate the frequency of revolution of an electron in a hydrogen atom assuming that the radius of the first Bohr orbit is `5 xx 10^(-11)`m. Mass of electron `= 9.0 xx 10^(-31) kg` , charge of electron `= 1.6 xx 10^(-19) C, (1)/(4pi epsilon_(0))=9xx10^(9) SI` units.

A body is suspended by a string of length 1 m and is projected horizontally with a velocity of `4 ms^(-1)` Calculate its tangential and radial accelerations when the string rises by `60^(@)` from its initial position.

The bob of a simple pendulum of length 1m hangs at rest. It is suddenly projected horizontally with velocity `10 ms^(-1)`. Calculate the velocity of the bob and tension of the string when it is horizontal. The mass of the bob is `(1)/(2)`kg. [Hint : See worked out example 4]

In problem 17 if the mass `m` is allowed to fall from a height `2R`, find the reaction of the track on the sliding mass the lowest point, at the highest point, at the mid-point. Take `R : r = 5:2`

A particle of mass m is suspended by a string of length l from a fixed rigid support. Particle is imparted a horizontal velocity `u=sqrt(2gl)`. Find the angle made by the string with the vertical when the acceleration of the particle is inclined to the string by `45^(@)`?

If a simple pendulum of mass `m` is released from a horizontal position, find the tension in the string as a function of the angle `theta` with the horizontal.

In the figure of problem 17 if the block starts from rest when `R = 5r`, what is the reaction of the inner track on the sliding mass at the highest point ? From what height should it fall so that it may exert a force equal to its weight on the track at the highesth point ?

A ring of mass `m` and radius `R` is being rotated about its axis with constant angular velocity `omega` in the gravity free space. Find tension in the ring.

A bucket containing water is tied to one end of a rope 2 m long and rotated in a circle about the other end in a vertical plane. Find the minimum number of rotations per minute in order that water may not spill. `(g = 9.8 ms^(-2))`.