JEE Main 2021 (Online) 27th July Evening Shift | Gravitation Question 98 | Physics

The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 $$\times$$ 10³ km. Find the mass of Mars.

$$\left\{ {Given\,{{4{\pi ^2}} \over G} = 6 \times {{10}^{11}}{N^{ - 1}}{m^{ - 2}}k{g^2}} \right\}$$

5.96 $$\times$$ 10¹⁹ kg

3.25 $$\times$$ 10²¹ kg

7.02 $$\times$$ 10²⁵ kg

6.00 $$\times$$ 10²³ kg

JEE Main 2021 (Online) 25th July Evening Shift

MCQ (Single Correct Answer)

-1

Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be :

$${2^{{1 \over 3}}}$$W

$$\sqrt 2 $$W

JEE Main 2021 (Online) 25th July Morning Shift

MCQ (Single Correct Answer)

-1

The minimum and maximum distances of a planet revolving around the sun are x₁ and x₂. If the minimum speed of the planet on its trajectory is v₀ then its maximum speed will be :

$${{{v_0}x_1^2} \over {x_2^2}}$$

$${{{v_0}x_2^2} \over {x_1^2}}$$

$${{{v_0}x_1^{}} \over {x_2^{}}}$$

$${{{v_0}x_2^{}} \over {x_1^{}}}$$

JEE Main 2021 (Online) 22th July Evening Shift

MCQ (Single Correct Answer)

-1

A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height h is ___________ s.

$$\sqrt {{{2{R_e}} \over g}} \left[ {{{\left( {1 + {h \over {{R_e}}}} \right)}^{{3 \over 2}}} - 1} \right]$$

$${1 \over 3}\sqrt {{{{R_e}} \over {2g}}} \left[ {{{\left( {1 + {h \over {{R_e}}}} \right)}^{{3 \over 2}}} - 1} \right]$$

$$\sqrt {{{{R_e}} \over {2g}}} \left[ {{{\left( {1 + {h \over {{R_e}}}} \right)}^{{3 \over 2}}} - 1} \right]$$

$${1 \over 3}\sqrt {{{2{R_e}} \over g}} \left[ {{{\left( {1 + {h \over {{R_e}}}} \right)}^{{3 \over 2}}} - 1} \right]$$

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