NEET

Which of the following quantities do not depend upon the \(\frac{T}{R}\) orbital radius of the satellite ?

\(\frac{T}{R}\)
\(\frac{T}{R}\)
\(\frac{T}{R}\)
\(\frac{T^{2}}{R^{3}}\)

Solution

According to 3^rd law of Kepler

T²αR²

⇒T²=KR³

where K is a constant

Thus\(\frac{T^{2}}{R^{3}}\)does not depends on radius.

The orbital velocity of an artificial satellite in a circular orbit very close to Earth is v. The velocity of a geosynchronous satellite orbiting in a circular orbit at an altitude of 6R from Earth’s surface will be

\(\frac{v}{\sqrt{7}}\)
\(\frac{v}{\sqrt{7}}\)
v
\(\sqrt{6}\)v

Solution

\(v_{1}\alpha \frac{1}{\sqrt{R}},V_{2}\alpha \frac{1}{\sqrt{7R}}\)

\(\frac{v_{2}}{v_{1}}=\frac{1}{\sqrt{7}}\Rightarrow v_{2}=\frac{v_{1}}{\sqrt{7}}=\frac{v}{\sqrt{7}}\)

Escape velocity when a body of mass m is thrown vertically from the surface of the earth is v, what will be the escape velocity of another body of mass 4 m is thrown vertically

v
2v
4v
None of these

Solution

Escape velocity does not depend upon the mass of the body

The distance of neptune and saturn from the sun is nearly 10¹³ and 10¹² meter respectively.As suming that they move in circular orbits, their periodic times will be in the ratio

10
100
10\(\sqrt{10}\)
1000

Solution

\(T^{2}\alpha R^{3}(According\: to \: Kepler’s \: law)\)

\(T^{2}\alpha R^{3}(According\: to \: Kepler’s \: law)\)

\(∴\frac{T_{1}^{2}}{T_{2}^{2}}=(10)^{3}\: or\: \frac{T_{1}}{T_{2}}=10\sqrt{10}\)

Directions: Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following

Statement -1:Gravitational potential is maximum at infinity.

Statement -2 :Gravitational potential is the amount of work done to shift a unit mass from infinity to a given point in gravitational attraction force field.

(a)Statement -1 is false, Statement-2 is true
(b)Statement -1 is true, Statement-2 is true;Statement -2 is a correct explanation for Statement-1
(c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
(d)Statement -1 is true, Statement-2 is false

Solution

(b)Statement -1 is true, Statement-2 is true;Statement -2 is a correct explanation for Statement-1

Directions: Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following

Statement -1 : For the planets orbiting around the sun,angular speed, linear speed and K.E. changes with time,but angular momentum remains constant.

Statement -2 : No torque is acting on the rotating planet.So its angular momentum is constant.

(a)Statement -1 is false, Statement-2 is true
(b)Statement -1 is true, Statement-2 is true;Statement -2 is a correct explanation for Statement-1
(c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
(d)Statement -1 is true, Statement-2 is false

Solution

(b) Statement -1 is true, Statement-2 is true;Statement -2 is a correct explanation for Statement-1

Directions: Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following

Statement -1 :The escape speed does not depend on the direction in which the projectile is fired.

Statement -2 :Attaining the escape speed is easier if a projectile is fired in the direction the launch site is moving as the earth rotates about its axis.

(a)Statement -1 is false, Statement-2 is true
(b)Statement -1 is true, Statement-2 is true;Statement -2 is a correct explanation for Statement-1
(c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
(d)Statement -1 is true, Statement-2 is false

Solution

(c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1

Directions: Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following

Statement -1 : If an object is projected from earth surface with escape velocity path of object will be parabola.

Statement -2 :When object is projected with velocity less than escape velocity from horizontal surface and greaterthan orbital velocity. Path of object will be ellipse.

(a)Statement -1 is false, Statement-2 is true
(b)Statement -1 is true, Statement-2 is true;Statement -2 is a correct explanation for Statement-1
(c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
(d)Statement -1 is true, Statement-2 is false

Solution

(c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1

Directions: Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following

Statement -1 : Space rockets are usually launched in the equatorial line from west to east.

Statement -2 : The acceleration due to gravity is minimum at the equator.

(a)Statement -1 is false, Statement-2 is true
(b)Statement -1 is true, Statement-2 is true;Statement -2 is a correct explanation for Statement-1
(c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
(d)Statement -1 is true, Statement-2 is false

Solution

(c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1

The speed of earth’s rotation about its axis is ω. Its speed is increased to x times to make the effective acceleration due to gravity equal to zero at the equator. Then x is

1
8.5
17
34

Solution

g'= g – ω² R cos² λ(for equator λ = 0°)

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