QBManager

Gravitation

138236 Three particles each of mass $m$ are kept at vertices of an equilateral triangle of side $L$ . The gravitational field at centre due to these particles is

1 zero

2

\frac{3 GM}{L^{2}}

3

\frac{9 GM}{L^{2}}

4

\frac{12}{\sqrt{3}} \frac{GM}{L^{2}}

Explanation:

A
In equilateral triangle all sides are equal i.e. $AB = BC =$ $CA$ and the line joining the centre of gravity to each vertex of the triangle are each at angle $120^{\circ}$ and gravitational field by each mass will be along these lines joining the centre and vertex. As triangle is equilateral, then the gravitational field produced by each mass will be same. Gravitational field produced is equal in magnitude and at an angle $120^{\circ}$ . So, net field will be zero.

Manipal UGET-2010

Gravitation

138244 A satellite orbiting around the certain planet has apogee $R_{1}$ and perigee equal to $R_{2}$ , then find the minimum kinetic energy that should be given to the satellite to enable it to escape from the planet.

1

\frac{GMm}{(R_{1} + R_{2})}

2

\frac{2 GMm}{(R_{1} + R_{2})}

3

\frac{GMm}{2 (R_{1} + R_{2})}

4

\frac{GMm}{3 (R_{1} + R_{2})}

Explanation:

C $\overset{R_{1} \to}{*} \leftarrow R_{2} \to$
$r = R_{1} + R_{2}$
$∵$ T. E. $= \frac{- GMm}{2 r}$
K. $E =∣$ T. E. $| = | - \frac{GMm}{2 r} ∣= \frac{GMm}{2 (R_{1} + R_{2})}$

AIIMS-26.05.2018(M)

Gravitation

138248 The gravitational force with which the earth attracts the moon

1 is less than the force with which the moon attracts the earth

2 is equal to the force with which the moon attracts the earth

3 is twice than the force with which the moon attracts the earth

4 varies with the phases of moon

Explanation:

B Gravitational force between two objects of masses $m_{1}$ and $m_{2}$ separated by distance $r$ is given by
$F_{g} = \frac{{Gm}_{1} m_{2}}{r^{2}}$
This force is same for both the objects. If earth attracts moon with a Force F, then moon also attracts the earth with the same Force F.

J and K CET- 2002

Gravitation

138251 If the earth were to rotate faster than its present speed, the weight of an object will

1 Increase at the equator but remain unchanged at the poles

2 Decrease at the equator but remain unchanged at the poles

3 Decrease at the poles but remain unchanged at the equator

4 Increase at the pole but remain unchanged at the equator

JCECE-2013

Gravitation

138254 Which of the following forces have the infinite range?

1 Gravitational Force, Nuclear Force and Electromagnetic Force

2 Gravitational Force and Nuclear Force Only

3 Nuclear Force and Electromagnetic Force Only

4 Electromagnetic Force and Gravitational Force Only

Explanation:

D The range of gravitational force and electromagnetic forces are till infinite.
We know that,
Gravitational force $(F_{g}) = \frac{{Gm}_{1} m_{2}}{r^{2}} F_{g} \to 0$ if $r \to \infty$
Electrostatic force $(F_{e}) = \frac{{Kq}_{1} q_{2}}{r^{2}} F_{e} \to 0$ if $r \to \infty$

TS EAMCET 31.07.2022

Gravitation

138236 Three particles each of mass $m$ are kept at vertices of an equilateral triangle of side $L$ . The gravitational field at centre due to these particles is

1 zero

2

\frac{3 GM}{L^{2}}

3

\frac{9 GM}{L^{2}}

4

\frac{12}{\sqrt{3}} \frac{GM}{L^{2}}

Explanation:

A
In equilateral triangle all sides are equal i.e. $AB = BC =$ $CA$ and the line joining the centre of gravity to each vertex of the triangle are each at angle $120^{\circ}$ and gravitational field by each mass will be along these lines joining the centre and vertex. As triangle is equilateral, then the gravitational field produced by each mass will be same. Gravitational field produced is equal in magnitude and at an angle $120^{\circ}$ . So, net field will be zero.

Manipal UGET-2010

Gravitation

138244 A satellite orbiting around the certain planet has apogee $R_{1}$ and perigee equal to $R_{2}$ , then find the minimum kinetic energy that should be given to the satellite to enable it to escape from the planet.

1

\frac{GMm}{(R_{1} + R_{2})}

2

\frac{2 GMm}{(R_{1} + R_{2})}

3

\frac{GMm}{2 (R_{1} + R_{2})}

4

\frac{GMm}{3 (R_{1} + R_{2})}

Explanation:

C $\overset{R_{1} \to}{*} \leftarrow R_{2} \to$
$r = R_{1} + R_{2}$
$∵$ T. E. $= \frac{- GMm}{2 r}$
K. $E =∣$ T. E. $| = | - \frac{GMm}{2 r} ∣= \frac{GMm}{2 (R_{1} + R_{2})}$

AIIMS-26.05.2018(M)

Gravitation

138248 The gravitational force with which the earth attracts the moon

1 is less than the force with which the moon attracts the earth

2 is equal to the force with which the moon attracts the earth

3 is twice than the force with which the moon attracts the earth

4 varies with the phases of moon

Explanation:

B Gravitational force between two objects of masses $m_{1}$ and $m_{2}$ separated by distance $r$ is given by
$F_{g} = \frac{{Gm}_{1} m_{2}}{r^{2}}$
This force is same for both the objects. If earth attracts moon with a Force F, then moon also attracts the earth with the same Force F.

J and K CET- 2002

Gravitation

138251 If the earth were to rotate faster than its present speed, the weight of an object will

1 Increase at the equator but remain unchanged at the poles

2 Decrease at the equator but remain unchanged at the poles

3 Decrease at the poles but remain unchanged at the equator

4 Increase at the pole but remain unchanged at the equator

JCECE-2013

Gravitation

138254 Which of the following forces have the infinite range?

1 Gravitational Force, Nuclear Force and Electromagnetic Force

2 Gravitational Force and Nuclear Force Only

3 Nuclear Force and Electromagnetic Force Only

4 Electromagnetic Force and Gravitational Force Only

Explanation:

D The range of gravitational force and electromagnetic forces are till infinite.
We know that,
Gravitational force $(F_{g}) = \frac{{Gm}_{1} m_{2}}{r^{2}} F_{g} \to 0$ if $r \to \infty$
Electrostatic force $(F_{e}) = \frac{{Kq}_{1} q_{2}}{r^{2}} F_{e} \to 0$ if $r \to \infty$

TS EAMCET 31.07.2022

Gravitation

138236 Three particles each of mass $m$ are kept at vertices of an equilateral triangle of side $L$ . The gravitational field at centre due to these particles is

1 zero

2

\frac{3 GM}{L^{2}}

3

\frac{9 GM}{L^{2}}

4

\frac{12}{\sqrt{3}} \frac{GM}{L^{2}}

Explanation:

A
In equilateral triangle all sides are equal i.e. $AB = BC =$ $CA$ and the line joining the centre of gravity to each vertex of the triangle are each at angle $120^{\circ}$ and gravitational field by each mass will be along these lines joining the centre and vertex. As triangle is equilateral, then the gravitational field produced by each mass will be same. Gravitational field produced is equal in magnitude and at an angle $120^{\circ}$ . So, net field will be zero.

Manipal UGET-2010

Gravitation

138244 A satellite orbiting around the certain planet has apogee $R_{1}$ and perigee equal to $R_{2}$ , then find the minimum kinetic energy that should be given to the satellite to enable it to escape from the planet.

1

\frac{GMm}{(R_{1} + R_{2})}

2

\frac{2 GMm}{(R_{1} + R_{2})}

3

\frac{GMm}{2 (R_{1} + R_{2})}

4

\frac{GMm}{3 (R_{1} + R_{2})}

Explanation:

C $\overset{R_{1} \to}{*} \leftarrow R_{2} \to$
$r = R_{1} + R_{2}$
$∵$ T. E. $= \frac{- GMm}{2 r}$
K. $E =∣$ T. E. $| = | - \frac{GMm}{2 r} ∣= \frac{GMm}{2 (R_{1} + R_{2})}$

AIIMS-26.05.2018(M)

Gravitation

138248 The gravitational force with which the earth attracts the moon

1 is less than the force with which the moon attracts the earth

2 is equal to the force with which the moon attracts the earth

3 is twice than the force with which the moon attracts the earth

4 varies with the phases of moon

Explanation:

B Gravitational force between two objects of masses $m_{1}$ and $m_{2}$ separated by distance $r$ is given by
$F_{g} = \frac{{Gm}_{1} m_{2}}{r^{2}}$
This force is same for both the objects. If earth attracts moon with a Force F, then moon also attracts the earth with the same Force F.

J and K CET- 2002

Gravitation

138251 If the earth were to rotate faster than its present speed, the weight of an object will

1 Increase at the equator but remain unchanged at the poles

2 Decrease at the equator but remain unchanged at the poles

3 Decrease at the poles but remain unchanged at the equator

4 Increase at the pole but remain unchanged at the equator

JCECE-2013

Gravitation

138254 Which of the following forces have the infinite range?

1 Gravitational Force, Nuclear Force and Electromagnetic Force

2 Gravitational Force and Nuclear Force Only

3 Nuclear Force and Electromagnetic Force Only

4 Electromagnetic Force and Gravitational Force Only

Explanation:

D The range of gravitational force and electromagnetic forces are till infinite.
We know that,
Gravitational force $(F_{g}) = \frac{{Gm}_{1} m_{2}}{r^{2}} F_{g} \to 0$ if $r \to \infty$
Electrostatic force $(F_{e}) = \frac{{Kq}_{1} q_{2}}{r^{2}} F_{e} \to 0$ if $r \to \infty$

TS EAMCET 31.07.2022

Gravitation

138236 Three particles each of mass $m$ are kept at vertices of an equilateral triangle of side $L$ . The gravitational field at centre due to these particles is

1 zero

2

\frac{3 GM}{L^{2}}

3

\frac{9 GM}{L^{2}}

4

\frac{12}{\sqrt{3}} \frac{GM}{L^{2}}

Explanation:

A
In equilateral triangle all sides are equal i.e. $AB = BC =$ $CA$ and the line joining the centre of gravity to each vertex of the triangle are each at angle $120^{\circ}$ and gravitational field by each mass will be along these lines joining the centre and vertex. As triangle is equilateral, then the gravitational field produced by each mass will be same. Gravitational field produced is equal in magnitude and at an angle $120^{\circ}$ . So, net field will be zero.

Manipal UGET-2010

Gravitation

138244 A satellite orbiting around the certain planet has apogee $R_{1}$ and perigee equal to $R_{2}$ , then find the minimum kinetic energy that should be given to the satellite to enable it to escape from the planet.

1

\frac{GMm}{(R_{1} + R_{2})}

2

\frac{2 GMm}{(R_{1} + R_{2})}

3

\frac{GMm}{2 (R_{1} + R_{2})}

4

\frac{GMm}{3 (R_{1} + R_{2})}

Explanation:

C $\overset{R_{1} \to}{*} \leftarrow R_{2} \to$
$r = R_{1} + R_{2}$
$∵$ T. E. $= \frac{- GMm}{2 r}$
K. $E =∣$ T. E. $| = | - \frac{GMm}{2 r} ∣= \frac{GMm}{2 (R_{1} + R_{2})}$

AIIMS-26.05.2018(M)

Gravitation

138248 The gravitational force with which the earth attracts the moon

1 is less than the force with which the moon attracts the earth

2 is equal to the force with which the moon attracts the earth

3 is twice than the force with which the moon attracts the earth

4 varies with the phases of moon

Explanation:

B Gravitational force between two objects of masses $m_{1}$ and $m_{2}$ separated by distance $r$ is given by
$F_{g} = \frac{{Gm}_{1} m_{2}}{r^{2}}$
This force is same for both the objects. If earth attracts moon with a Force F, then moon also attracts the earth with the same Force F.

J and K CET- 2002

Gravitation

138251 If the earth were to rotate faster than its present speed, the weight of an object will

1 Increase at the equator but remain unchanged at the poles

2 Decrease at the equator but remain unchanged at the poles

3 Decrease at the poles but remain unchanged at the equator

4 Increase at the pole but remain unchanged at the equator

JCECE-2013

Gravitation

138254 Which of the following forces have the infinite range?

1 Gravitational Force, Nuclear Force and Electromagnetic Force

2 Gravitational Force and Nuclear Force Only

3 Nuclear Force and Electromagnetic Force Only

4 Electromagnetic Force and Gravitational Force Only

Explanation:

D The range of gravitational force and electromagnetic forces are till infinite.
We know that,
Gravitational force $(F_{g}) = \frac{{Gm}_{1} m_{2}}{r^{2}} F_{g} \to 0$ if $r \to \infty$
Electrostatic force $(F_{e}) = \frac{{Kq}_{1} q_{2}}{r^{2}} F_{e} \to 0$ if $r \to \infty$

TS EAMCET 31.07.2022

Gravitation

138236 Three particles each of mass $m$ are kept at vertices of an equilateral triangle of side $L$ . The gravitational field at centre due to these particles is

1 zero

2

\frac{3 GM}{L^{2}}

3

\frac{9 GM}{L^{2}}

4

\frac{12}{\sqrt{3}} \frac{GM}{L^{2}}

Explanation:

A
In equilateral triangle all sides are equal i.e. $AB = BC =$ $CA$ and the line joining the centre of gravity to each vertex of the triangle are each at angle $120^{\circ}$ and gravitational field by each mass will be along these lines joining the centre and vertex. As triangle is equilateral, then the gravitational field produced by each mass will be same. Gravitational field produced is equal in magnitude and at an angle $120^{\circ}$ . So, net field will be zero.

Manipal UGET-2010

Gravitation

138244 A satellite orbiting around the certain planet has apogee $R_{1}$ and perigee equal to $R_{2}$ , then find the minimum kinetic energy that should be given to the satellite to enable it to escape from the planet.

1

\frac{GMm}{(R_{1} + R_{2})}

2

\frac{2 GMm}{(R_{1} + R_{2})}

3

\frac{GMm}{2 (R_{1} + R_{2})}

4

\frac{GMm}{3 (R_{1} + R_{2})}

Explanation:

C $\overset{R_{1} \to}{*} \leftarrow R_{2} \to$
$r = R_{1} + R_{2}$
$∵$ T. E. $= \frac{- GMm}{2 r}$
K. $E =∣$ T. E. $| = | - \frac{GMm}{2 r} ∣= \frac{GMm}{2 (R_{1} + R_{2})}$

AIIMS-26.05.2018(M)

Gravitation

138248 The gravitational force with which the earth attracts the moon

1 is less than the force with which the moon attracts the earth

2 is equal to the force with which the moon attracts the earth

3 is twice than the force with which the moon attracts the earth

4 varies with the phases of moon

Explanation:

B Gravitational force between two objects of masses $m_{1}$ and $m_{2}$ separated by distance $r$ is given by
$F_{g} = \frac{{Gm}_{1} m_{2}}{r^{2}}$
This force is same for both the objects. If earth attracts moon with a Force F, then moon also attracts the earth with the same Force F.

J and K CET- 2002

Gravitation

138251 If the earth were to rotate faster than its present speed, the weight of an object will

1 Increase at the equator but remain unchanged at the poles

2 Decrease at the equator but remain unchanged at the poles

3 Decrease at the poles but remain unchanged at the equator

4 Increase at the pole but remain unchanged at the equator

JCECE-2013

Gravitation

138254 Which of the following forces have the infinite range?

1 Gravitational Force, Nuclear Force and Electromagnetic Force

2 Gravitational Force and Nuclear Force Only

3 Nuclear Force and Electromagnetic Force Only

4 Electromagnetic Force and Gravitational Force Only

Explanation:

D The range of gravitational force and electromagnetic forces are till infinite.
We know that,
Gravitational force $(F_{g}) = \frac{{Gm}_{1} m_{2}}{r^{2}} F_{g} \to 0$ if $r \to \infty$
Electrostatic force $(F_{e}) = \frac{{Kq}_{1} q_{2}}{r^{2}} F_{e} \to 0$ if $r \to \infty$

TS EAMCET 31.07.2022