Q.1. A small block slides down on a smooth inclined plane starting from rest at time t=0. Let Sn be the distance travelled by the block in the interval t= n1 to t=n. Then the ratio is: [2021]
A:
B:
C:
D:
Ans: D
Solution:
Sn = Distance in n^{th }sec.
i.e. t = n – 1 to t = n
S_{n + 1} = Distance in (n + 1)^{th} sec.
i.e. t = n to t = n + 1
So as we know,
Q.2. A ball is thrown vertically downward with a velocity of 20m/s from the top of a tower. It hits the ground after some time with a velocity of 80m/s. The height of the tower is : (g = 10m/s^{2}) [2020]
A: 320 m
B: 300 m
C: 360 m
D: 340 m
Ans: B
v^{2} – u^{2} = 2as
(80)^{2} – (–20)^{2} = 2(–10) × s
6400 – 400 = 2 × (–10) × s
s = – 300 m
Height of tower h = 300 m
Q.3. Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t_{1}. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t_{2}. The time taken by her to walk up on the moving escalator will be [2017]
A:
B:
C: t_{1} – t_{2}
D:
Ans: B
Solution:
As we learnt in
Case of Relative velocity 
When A & B are moving along with straight line in opposite direction.
Relative velocity of A with respect to B is.
Q.4. A particle moves so that its position vector is given by r = cosωtx + sinωty. Where ω is a constant. Which of the following is true?
A: Velocity is perpendicular to r and acceleration is directed away from the origin.
B: Velocity and acceleration both are perpendicular to r
C: Velocity is acceleration both are parallel to r
D: Velocity is perpendicular to r and acceleration is directed towards the origin. [2016]
Ans: D
Solution:
Q.5. If the velocity of a particle is , where A and B are constants, then the distance travelled by it between 1s and 2s is [2016]
A: A/2 + B/3
B: 3A/2 + B
C: 3A + 7B
D: 3A/2 + 7B/3
Ans: D
Solution:
Q.6. A particle of unit mass undergoes onedimensional motion such that its velocity varies according to v(x) = βx^{2n}, where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by : [2015]
A: 2nβ^{2} e^{4n + 1}
B: 2nβ^{2} x^{2n  1}
C: 2nβ^{2} x^{4n  1}
D: 2nβ^{2} x^{2n + 1}
Ans: C
Solution:
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