1
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, TA/TB, is ;
A
2
B
$${{1 \over 2}}$$
C
$$\sqrt {{1 \over 2}}$$
D
1
2
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass 'm' at x = 0, if the mass per unit length of the rod is A + Bx2 , is given by :
A
$$Gm\left[ {A\left( {{1 \over a} - {1 \over {a + L}}} \right) - BL} \right]$$
B
$$Gm\left[ {A\left( {{1 \over a} - {1 \over {a + L}}} \right) + BL} \right]$$
C
$$Gm\left[ {A\left( {{1 \over {a + L}} - {1 \over a}} \right) + BL} \right]$$
D
$$Gm\left[ {A\left( {{1 \over {a + L}} - {1 \over a}} \right) - BL} \right]$$
3
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be :
A
in the same circular orbit of radius R
B
such that it escapes to infinity
C
in a circular orbit of a different radius
D
in an elliptical orbit
4
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
A satellite is revolving in a circular orbit at a height h form the earth surface, such that h < < R where R is the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is :
A
$$\sqrt {gR} \left( {\sqrt 2 - 1} \right)$$
B
$$\sqrt {2gR}$$
C
$$\sqrt {gR}$$
D
$${{\sqrt {gR} } \over 2}$$
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