MAXIMUM MARKS: 25 TIME ALLOWED: 30 MINUTES
Q1.
Check the accuracy of the relation v

1 T
2 l M tension and m is mass of unit length of the string.
, where v is the frequency, l is the length, T is the
Q2.
In Van der Waal’s equation: p
 a
V
2
( V
 b _

RT , what are the dimensions of a and b? Here, p is pressure, V is volume, T is temperature and R is gas constant.
Q3.
The time of oscillation‘t’ of a small drop of a liquid under surface tension (s) depends upon the density d, the radius r, and the surface tension s. Prove dimensionally that t
 dr
3
.
s
Q4.
The centripetal force F acting on particle moving uniformly in a circle may depend upon mass (m), velocity (v) and radius (r) of the circle. Derive the formula for F using the method of dimensions.
Q5.
A wave is set up in a stretched, string by plucking it. The velocity v of the wave depends upon tension F in the string, its length‘t’ and its mass ‘m’. Making use of the knowledge of dimensions, prove that: v

Tension
Mass per unit length
Q6.
Which of the following equations are dimensionally correct?
(i) Pressure = Energy per unit volume.
(ii) Pressure = Energy per unit area.
(iii) Pressure = Force per unit area.
(iv) Pressure = Momentum

volume
 time
What are the limitations of dimensional analysis?
Q7. Describe the nature of motion represented by the following graph:
Q8. The position-time (x-t) graphs for two children A and B returning from their second O to their homes P and Q respectively are shown in the fig. alongside. Choose the correct entries in the brackets below: (a) (A/B) lives closer to the school than (B/A). (b) (A/B) walks faster than (B/A).
(c) (A/B) walks faster than (B/A). (d) A and B reach home at the (same/different) time.
(e) (A/B) overtakes (B/A) on the road (once/twice).
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MAXIMUM MARKS: 25 TIME ALLOWED: 30 MINUTES
Q9.
What do the following velocity-time graphs represent? Explain the nature of motion of the body in each case
Q10. Suggest a suitable physical situation for each of the graphs drawn alongside.
Q11. Derive an equation for the distance travelled by a uniformly accelerated body in n th second of its motion.
Q12. If a,b,c be the distance travelled by a particle moving with a constant acceleration during the lth, mth, and nth seconds of its motion respectively. Show that a(m – n) + b(n – 1) + c(l – m) = 0.
Q13.
A three-wheeler starts from rest accelerated uniformly with 1 ms -2 on a straight road for
10 seconds, and then moves with uniform velocity. Plot the distance covered by the vehicle during the nth second (n=1,2,3….) versus n. What do you expect this plot to be during accelerated motion: a straight line or a parabola?
Q14. The velocity of the engine and last compartment of a train passing through a pole is u and v respectively. What is the velocity of middle compartment of the train?
Q15. The (x-t) graph of a moving particle is shown in the figure below. Comment on the signs of the velocities at the points C,D, E and F.
Q16. A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward and so on.
Each step is 1 m long and requires 1s. Plot the x-t graph of his motion. Determine graphically and otherwise how long the drunkard takes do fall in a pit 13 m away from the start.
Q17. A motor car covers 1/3 part of the total distance with velocity v
1
= kmh -1 and second 1/3 part with velocity, v
2
=20 kmh -1 and rest 1/3 part with velocity, v
3
=60 kmh -1 . What is the average speed of the car?
Q18. On a two-lane road, car A is travelling with a speed of 36 kmh -1 . Two car B and C approach car
A in opposite directions with a speed of 54 kmh -1 each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decide to overtake A before C does. What minimum acceleration of car B is required to avoid an accident?
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