1
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
A particle moving in the xy plane experiences a velocity dependent force
$$\overrightarrow F = k\left( {{v_y}\widehat i + {v_x}\widehat j} \right)$$ , where vx and vy are the
x and y components of its velocity $$\overrightarrow v$$ . If $$\overrightarrow a$$ is the
acceleration of the particle, then
which of the following statements is true for the particle?
A
kinetic energy of particle is constant in time
B
quantity $$\overrightarrow v \times \overrightarrow a$$ is constant in time
C
quantity $$\overrightarrow v .\overrightarrow a$$ is constant in time
D
$$\overrightarrow F$$ arises due to a magnetic field
2
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is :
(g = 10 ms–2)
A
0.45 m
B
0.60 m
C
0.20 m
D
0.80 m
3
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
$$- {{b{v^3}} \over {2M\left( t \right)}}$$
4
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
$${1 \over k}\ln \left( {1 + {{k{u^2}} \over {2g}}} \right)$$
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