JEE Mains Previous Year Questions (2026)): Laws of Motion

Q1: A particle moving in the xy plane experiences a velocity dependent force  , where v_x and v_y are the x and y components of its velocity  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  is constant in time
(c) quantity  is constant in time
(d)  arises due to a magnetic field
Ans: (b)


From Option (B),

= Constant

Q2: 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
Ans: (c)
For balancing mgsin θ = f
mgsin θ = μ mgcos θ
⇒ tan θ = μ = 3/4
h = R - R cos θ



Q3: A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate  where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is :
(a) -bv³(t)
(b)
(c)
(d)
Ans: (c)

In free space no external force so there in only thrust force on rocket.

Force on satellite
M(t)a = - v (bv²)


Q4: 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)
(b)
(c)
(d)
Ans: (c)
F_net = ma


Q5: 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 45^o 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
Ans: (b)
For equilibrium,
T sin 45^o = F ....(1)
and T cos 45^o = 10g ....(2)
Performing (1)/(2)
we get F = 10g = 100 N