1
JEE Main 2020 (Online) 5th September Evening Slot
+4
-1
A spaceship in space sweeps stationary interplanetary dust. As a result, its mass
increases at a rate $${{dM\left( t \right)} \over {dt}}$$ = bv2(t), where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is :
A
-bv3(t)
B
$$- {{2b{v^3}} \over {M\left( t \right)}}$$
C
$$- {{b{v^3}} \over {M\left( t \right)}}$$
D
$$- {{b{v^3}} \over {2M\left( t \right)}}$$
2
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force mkv2 where v is its speed. The maximum height attained by the ball is :
A
$${1 \over k}{\tan ^{ - 1}}{{k{u^2}} \over {2g}}$$
B
$${1 \over {2k}}{\tan ^{ - 1}}{{k{u^2}} \over g}$$
C
$${1 \over {2k}}\ln \left( {1 + {{k{u^2}} \over g}} \right)$$
D
$${1 \over k}\ln \left( {1 + {{k{u^2}} \over {2g}}} \right)$$
3
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid point of the rope such that the top half of the rope makes an angle of 45o with the vertical. Then F equal : (Take g = 10 ms–2 and the rope to be massless)
A
100 N
B
75 N
C
90 N
D
70 N
4
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F = 20 N, making an angle of 30o with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $$\mu$$ = 0.2. The difference between the accelerations of the blocks, in case (B) and case (A) will be : (g = 10 ms–2)
A
3.2 ms–2
B
0.8 ms–2
C
0 ms–2
D
0.4 ms–2
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