Tag: circular motion and gravitation

Questions Related to circular motion and gravitation

A body attached to a string of length describes a vertical circle such that it is just able to cross the highest point. Find the minimum velocity at the bottom of the circle.

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

  1. $\sqrt { 2gL } $

  2. $\sqrt { gL } $

  3. $\sqrt { 3gL } $

  4. $\sqrt { 5gL } $

Show answer
Correct Option: B
Explanation:
Radius of the circle traced will be equal to the length of the string
In circular motion tension in the string is balanced by the centripetal force
hence we know that,
$T=\dfrac { m{ v }^{ 2 } }{ r } $ 
$T=\dfrac { m{ v }^{ 2 } }{ L } $
Velocity at any point,$V=\sqrt { \dfrac { TL }{ m }  } $
And at lowest point the tension is balanced by the weight of the block
∴∴ tension = weight = mg
$V=\sqrt { \dfrac { mgL }{ m }  } =\sqrt { gL } $

A bucket is whirled in a vertical circle with a string attached to it. The water in the bucket does not fall down even when the bucket is inverted at the top of its path. We can say that in this position.

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

  1. $mg=\displaystyle\frac{mv^2}{r}$

  2. mg is greater than $\displaystyle\frac{mv^2}{r}$

  3. mg is not greater than $\displaystyle\frac{mv^2}{r}$

  4. mg is not less than $\displaystyle\frac{mv^2}{r}$

Show answer
Correct Option: A,C
Explanation:

When the bucket is at the top of its path, the forces acting on the water are gravity and centripetal force. Since, the water does not fall down. Therefore, centripetal force is greater than the force of gravity.

Therefore, $\cfrac{mV^2}{R}\ge mg$

Electrical, as well as gravitational affects, can be thought to be caused by fields. Which of the following is true of an electrical or gravitational field?

physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

  1. The field concept is often used to describe contact forces

  2. Gravitational or electric field does not exist in the space around an object

  3. Fields are useful for understanding forces acting through a distance

  4. There is no way to verify the existence of a force field since it is just a concept

Show answer
Correct Option: C
Explanation:

In physics, concept of field is a model used to explain the influence that a massive body or charged particle extends into the space around itself, producing a force on another massive body or charged body placed in space. Thus, concept of field is used to explain gravitational and electrostatic phenomena.

A satellite is revolving in a circular orbit at a height $'h'$ from the earth's surface (radius of earth $R$;$h\ <\ <\ R$). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to:(Neglect the effect of atmosphere.)

physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

  1. $\sqrt{2gR}$

  2. $\sqrt{gR}$

  3. $\sqrt{gR/2}$

  4. $\sqrt{gR}\left(\sqrt{2}-1\right)$

Show answer
Correct Option: D
Explanation:

height$=h$

No, the given formula,
Orbital velocity
$v=\cfrac{GM}{R+h}=\cfrac{GM}{R}$ as $h<<R$
Velocity required to escape
$\cfrac{1}{2}mv^{\prime 2}=\cfrac{GMm}{R+h}\v^{\prime}=\cfrac{2GM}{R+h}=\cfrac{2GM}{R}(h<<R)$
$\therefore$ Increase in velocity
$v^{\prime}=v=\sqrt{\cfrac{2GM}{R}}-\sqrt{\cfrac{GM}{R}}\ \quad=\sqrt{2gR}-\sqrt{gR}=\sqrt{gR}(\sqrt2-1)$

A force of 10 N of gravitational force in CGS units is  represented as

physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

  1. $10 Dynes$

  2. $10^2 Dynes$

  3. $10^5 Dynes$

  4. $10^6 Dynes$

Show answer
Correct Option: A
Explanation:

A force of 10 N of gravittional force in CGS units is represented by 10 Dynes.

Dyne is a CGS unit of force which accelerates a mass of one gram at the rate of one centimeter per second.

The presence of gravitational field is required for the heat transfer by

physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

  1. $conduction$

  2. $striring\ of\ liquids$

  3. $natural\ convection$

  4. $radiation$

Show answer
Correct Option: A
Explanation:

Presence of gravitational field is required for heat transfer by conduction.

The force experienced by a unit mass at a point in the gravitational field is called its

physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

  1. gravitational intensity

  2. electric intensity

  3. magnetic intensity

  4. gravitational constant

Show answer
Correct Option: A
Explanation:

The force experienced by a $unit $ mass at a point in the gravitational field $=F _g=mg=1\times g=g $ $ Newton $


We know that $g$ is called as gravitational intensity 

Hence correct answer is option $A $ 

The ratio of SI units to CGS of the gravitational intensity is

physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

  1. $10^3:1$

  2. infinity

  3. zero

  4. $10^2:1$

Show answer
Correct Option: D
Explanation:

Gravitational intensity is nothing but the acceleration due to gravity(g)

SI unit of g is $m/s^2=100cm/s^2$
But CGS unit of g is $cm/s^2$ 
So SI unit:CGS unit $=100:1$ 

Hence correct answer is option $D $ 

Which of the following represents the unit for gravitational intensity?

physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

  1. N

  2. $kgm^{-2}$

  3. $Nkg^{-1}$

  4. $ms^{-3}$

Show answer
Correct Option: C
Explanation:

Gravitational intensity is nothing but the acceleration due to gravity $=g=F _g/m$


Now we know that the SI unit of $F _g$ is $Newton(N) $ and that of $m$ is $kg$
So SI unit of $g=N/kg=Nkg^{-1}$ or $m/s^2$ 

Hence correct answer is option $C $ 

The space in which a body experiences a force by virtue of its mass, is called a/an

physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

  1. magnetic field

  2. electric field

  3. gravitational field

  4. none of these

Show answer
Correct Option: C
Explanation:

The region of space surrounding a body in which another body experiences a force of gravitational attraction is called a gravitational field.