1
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in the figure. If the mass A starts moving away from mass B with acceleration 'a', then the acceleration of mass B will be :

A
$${{MF} \over {F + Ma}}$$
B
$${{F + Ma} \over M}$$
C
$${{Ma - F} \over M}$$
D
$${{F - Ma} \over M}$$
2
JEE Main 2021 (Online) 24th February Evening Shift
+4
-1
A particle is projected with velocity v0 along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. ma = $$-$$ $$\alpha$$x2. The distance at which the particle stops :
A
$${\left[ {{{3mv_0^2} \over {2\alpha }}} \right]^{{1 \over 3}}}$$
B
$${\left( {{{2{v_0}} \over {3\alpha }}} \right)^{{1 \over 3}}}$$
C
$${\left( {{{3v_0^2} \over {2\alpha }}} \right)^{{1 \over 2}}}$$
D
$${\left( {{{2v_0^2} \over {3\alpha }}} \right)^{{1 \over 2}}}$$
3
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
4
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
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