JEE Main Previous year questions (2022): Circular Motion PDF Download

Q.1. A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and speed of the block (v) ?    (JEE Main 2022)
(a)
(b)
(c)
(d)

Ans. a
N = mv²/r
⇒ The graph given in option A suits the best for the above relation.

Q.2. A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be :    (JEE Main 2022)
(Given cos⁡135^∘ = −0.7)

(a) 42 m
(b) 47 m
(c) 19 m
(d) 40 m

Ans. b
Distance travelled = 60 m
⇒ Angle covered = 135^∘
Displacement = 2Rsin⁡(135^∘/2)

≈ 47 m

Q.3.  A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is K/π rev./min. The value of K is :
(Assume the string is massless and unstretchable)    (JEE Main 2022)
(a) 400
(b) 300
(c) 600
(d) 800

Ans. c
T = mω²r
⇒ 80 = 0.1 × (2π × K/π × 1/60)² × 2
⇒ 800/2 = K²/900
⇒ K = 30 × 20 = 600

Q.4. A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :    (JEE Main 2022)
(a) 7.5 rad
(b) 15 rad
(c) 20 rad
(d) 30 rad

Ans. b
θ₁ = 1/2α(2 × 1 − 1) = 5 rad
⇒ α = 10 rad/sec²
So θ₂ = 12 × α(2 × 2 − 1) = 15 rad

Q.5. A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is    (JEE Main 2022)
(a) the same throughout the motion.
(b) minimum at the highest position of the circular path.
(c) minimum at the lowest position of the circular path.
(d) minimum when the rope is in the horizontal position.

Ans. b

At any θ : T−mg cos⁡ θ = mv²/R
⇒ T = mg cos ⁡θ + mv²/R
Since v is constant,
⇒ T will be minimum when cosθ is minimum.
⇒ θ = 180∘ corresponds to T_minimum.

Q.6. For a particle in uniform circular motion, the accelerationat any point P(R, θ) on the circular path of radius R is (when θ is measured from the positive x-axis and v is uniform speed) :    (JEE Main 2022)
(a)
(b)
(c)
(d)

Ans. c

As the particle in uniform circular motion experiences only centripetal acceleration of magnitude ω²R or v²/R directed towards centre so from diagram,

Q.7. A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is α with respect to point P. Which of the following graphs represent the correct relation between A and α when ball goes from Q to R?    (JEE Main 2022)
(a)
(b)
(c)
(d)

Ans. c


Now, at Q ;
N − mg sin⁡ α = mac
N = m × 2g sin⁡ α +mg sin ⁡α
= 3mg sin⁡ α
= 2/3 = constant

Q.8. A stone tide to a spring of length L is whirled in a vertical circle with the other end of the spring at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is The value of x is -    (JEE Main 2022)
(a) 3
(b) 2
(c) 1
(d) 5

Ans. b

Q.9. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k²rt², where k is a constant. The power delivered to the particle by the force acting on it is given as    (JEE Main 2022)
(a) zero
(b) mk²r²t²
(c) mk²r²t
(d) mk²rt

Ans. c
ar = k²rt² = v²/r
⇒ v² = k²r²t² or v = krt
and d|v|/dt = kr
⇒ a_t = kr
⇒= (mkr)(krt)
= mk²r²t = power delivered

Q.10. A person starts his journey from centre 'O' of the park and comes back to the same position following path OPQO as shown in the figure. The radius of path taken by the person is 200 m and he takes 3 min 58 sec to complete his journey. The average speed of the person is _____________ ms⁻¹. (take π = 3.14)    (JEE Main 2022)

Ans. 3

Q.11. A curved in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be 30 m/s without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ___________ m/s.    (JEE Main 2022)

Ans. 24

⇒ V₂ = 24 m/s

Q.12. A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed v/3 and the bob just completes the vertical circle. The value of v is ___________ ms⁻¹. (if g = 10 m/s²).    (JEE Main 2022)

Ans. 10

Conserving momentum :
75 × v = 75 × v/3 + 50 × 10
⇒ 50v = 50 x 10
⇒ v = 10 m/s