Tag: circular motion and gravitation

Questions Related to circular motion and gravitation

Study of internal structure of earth is known is

physics circular motion and gravitation elementary ideas of astronomy shadow formation and optical medium light and shadow

  1. Mechanics

  2. Nuclear physics

  3. Atomic physics

  4. Geophysics

Show answer
Correct Option: D
Explanation:

Study of internal structure of earth is known is $Geophysics.$

Hence,
option $(D)$ is correct answer.

A satellite of mass $m$ is revolving around the earth at height $R$ (radius of the earth) from the earth's surface. Its potential energy will be :

physics circular motion and gravitation elementary ideas of astronomy shadow formation and optical medium light and shadow

  1. $mgR$

  2. $0.67 mgR$

  3. $-\dfrac{mgR}{2}$

  4. $0.33mgR$

Show answer
Correct Option: A

The tangential acceleration at particle at the lowest position is 

examples of circular motion uniform circular motion circular motion and gravitation physics

  1. 0

  2. 2 $m/{ s }^{ 2 }$

  3. 1 $m/{ s }^{ 2 }$

  4. None of these

Show answer
Correct Option: C

A small bucket containing water is rotated in a vertical circle of radius $R$ by means of a rope. $v$ is velocity of bucket at highest point. Then water does not fall down if:

examples of circular motion uniform circular motion circular motion and gravitation physics

  1. $v \leq \sqrt{gR}$

  2. $v \leq \sqrt{\frac{gR}{2}}$

  3. $v \geq \sqrt{gR}$

  4. $v \geq \sqrt{\frac{gR}{2}}$

Show answer
Correct Option: C
Explanation:

At highest point the centripetal acceleration should be greater than g.
$\therefore \dfrac{v^{2}}{R}\geq g$


or, $v\geq \sqrt{Rg}$

A bucket filled with water is tied to a rope of length $0.5\ m$ and is rotated in a circular path in vertical plane. the least velocity it should have at the lowest point of circle so that water does not spill is $(g=10ms^{-2})$:

examples of circular motion uniform circular motion circular motion and gravitation physics

  1. $\sqrt{5}\ m/s$

  2. $\sqrt{10}\ m/s$

  3. $5\ m/ s$

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

Show answer
Correct Option: C
Explanation:

Minimum velocity at bottom $V=\sqrt{5g\ell}$ $=\sqrt{5\times 10\times 0.5}$$=5:m/s$


A very small particle rests on the top of a hemisphere of radius $20\ cm$. The smallest horizontal velocity to be given to it, if it is to leave the hemisphere without sliding down its surface taking $g = 9.8 m/s^{2}$ is:

examples of circular motion uniform circular motion circular motion and gravitation physics

  1. $\sqrt{9.8}\ m/s$

  2. $\sqrt{4.9}\ m/s$

  3. $\sqrt{1.96}\ m/s$

  4. $\sqrt{3.92}\ m/s$

Show answer
Correct Option: C
Explanation:

Critical velocity at the top most point is $\sqrt{g\ell}$
$\therefore$ smallest velocity, such that the particle just leaves the surface =$\sqrt{9.8\times 0.2}=\sqrt{1.96}=1.4\ ms^{-1}$

The minimum centripetal force required to rotate a body mass $m$ in a vertical circle of radius $r$ is

examples of circular motion uniform circular motion circular motion and gravitation physics

  1. $mg$

  2. $2mg$

  3. $\dfrac{mg}{2}$

  4. Zero

Show answer
Correct Option: A
Explanation:

The tension at the top-most point would be zero in the critical case that the particle just completes the verticle circle without being slake. The minimum centripetal force would then be equal to the force due to gravity $=mg$


A particle of mass m is rotating by means of a string in a vertical circle. The difference in the tensions at the bottom and the top towards completion of a full revolution would be

examples of circular motion uniform circular motion circular motion and gravitation physics

  1. 6 mg

  2. 4 mg

  3. 5 mg

  4. 2 mg

Show answer
Correct Option: A
Explanation:

The tension at any point on the circular path is given by $T=(m/R)(u^2+gr-3gh)$; h is the height of the point from the horizontal

For a full circle, $h =2R$ Substituting, we get, $T _H=(m/R)(u^2-5gR)$ and 
at the bottom point of the circle , h=0 and thus, $T _L=(m/R)(u^2+gR)$

The difference in tension will be  $(T _L-T _H)=(m/R)(6gR) = 6mg$

Thus, the correct option is (a)

Four objects of masses m, 2m , 3m and 4m are attached to a string of length L=2 metres and rotated vertically with a speed of $\sqrt(5Lg)$, pick out the most appropriate one:

examples of circular motion uniform circular motion circular motion and gravitation physics

  1. m

  2. 2m

  3. 4m

  4. All the objects will complete the circle

Show answer
Correct Option: D
Explanation:

For an object to complete one full circle, the initial velocity should be atleast $\sqrt{5Lg}$. Thus, it is independent of the mass used

The correct option is (d)

An object suspended by a string has a critical velocity at the top most point of a circle. It will complete a full circle 

examples of circular motion uniform circular motion circular motion and gravitation physics

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Critical velocity is the minimum velocity at the top most point of a circle in which it is said to complete one full revolution. 

Thus, the statement is true