1
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
$$Gm\left[ {A\left( {{1 \over {a + L}} - {1 \over a}} \right) - BL} \right]$$
2
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
3
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
$${{\sqrt {gR} } \over 2}$$
4
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
Two stars of masses 3 $$\times$$ 1031 kg each, and at distance 2 $$\times$$ 1011 m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star’s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is - (Take Gravitational constant; G = 6.67 $$\times$$ 10–11 Nm2 kg–2)
A
2.4 $$\times$$ 104 m/s
B
1.4 $$\times$$ 105 m/s
C
3.8 $$\times$$ 104 m/s
D
2.8 $$\times$$ 105 m/s
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