1
JEE Main 2021 (Online) 25th July Morning Shift
+4
-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 :
A
$${{{v_0}x_1^2} \over {x_2^2}}$$
B
$${{{v_0}x_2^2} \over {x_1^2}}$$
C
$${{{v_0}x_1^{}} \over {x_2^{}}}$$
D
$${{{v_0}x_2^{}} \over {x_1^{}}}$$
2
JEE Main 2021 (Online) 22th July Evening Shift
+4
-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.
A
$$\sqrt {{{2{R_e}} \over g}} \left[ {{{\left( {1 + {h \over {{R_e}}}} \right)}^{{3 \over 2}}} - 1} \right]$$
B
$${1 \over 3}\sqrt {{{{R_e}} \over {2g}}} \left[ {{{\left( {1 + {h \over {{R_e}}}} \right)}^{{3 \over 2}}} - 1} \right]$$
C
$$\sqrt {{{{R_e}} \over {2g}}} \left[ {{{\left( {1 + {h \over {{R_e}}}} \right)}^{{3 \over 2}}} - 1} \right]$$
D
$${1 \over 3}\sqrt {{{2{R_e}} \over g}} \left[ {{{\left( {1 + {h \over {{R_e}}}} \right)}^{{3 \over 2}}} - 1} \right]$$
3
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
A satellite is launched into a circular orbit of radius R around earth, while a second satellite is launched into a circular orbit of radius 1.02 R. The percentage difference in the time periods of the two satellites is :
A
1.5
B
2.0
C
0.7
D
3.0
4
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
Consider a binary star system of star A and star B with masses mA and mB revolving in a circular orbit of radii rA an rB, respectively. If TA and TB are the time period of star A and star B, respectively,

Then :
A
$${{{T_A}} \over {{T_B}}} = {\left( {{{{r_A}} \over {{r_B}}}} \right)^{{3 \over 2}}}$$
B
$${T_A} = {T_B}$$
C
$${T_A} > {T_B}$$ (if $${m_A} > {m_B}$$)
D
$${T_A} > {T_B}$$ (if $${r_A} > {r_B}$$)
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