DIMENSIONAL ANALYSIS WORKSHEET

Question 1 The air bubble formed by explosion inside water perform oscillations with time period T which depends on pressure (p), density (ρ) and on energy due to explosion (E). Establish relation between T, p, E and ρ.

Question 2 The velocity v of a particle depends upon the time ‘t’ according to the equation V = (ab)^1/2 +bt + c/d+t 
Determine the units of a, b, c and d. What physical quantities they represent. All have SI units.

Question 3 The  position (x) of a particle at time t, is given by the 

relation, x(t)=v0/a(1-e-at), where v0 is a constant and a>0. Find the dimensions of v0 and a.

Question 4 The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by a relation f=cmxky; where c is a dimensionless quantity. Find the value of x and y.


Question 5 The time of oscillation t of a small drop of a liquid under surface tension depends upon the density d , radius r and surface tension S . Derive the expression for the time of oscillation of the drop using method of dimensions.

Question 6 Check the dimensional consistency in the following cases:

(a) mgh = F.v/t  -1/2 mv²

^(b) Tanθ = v²/rg  - cosθ

Question 7 If  X = at + bt²  where x is the distance travelled by the body in kilometre while t is the time in second, find the units of a and b.

Question 8 If energy (E), velocity (V) and time are chosen as fundamental quantities, 
what are the dimensions of surface tension?
Question 9 What are the dimensions of a/b in the equation P = a – t² / bx ? (where p is the pressure, x is the distance and t is time.)
Question 10 In the relation P = α e^αx/t/β , p is the pressure , x is distance and t is time. 
what are the dimensions of β?

Physics Problems for class 9 -Forces and laws of motion

This set of  Physics Problems for class 9  students of CBSE/ICSE/ State board covers Newtons's Law of motion, Force and  Linear motion. Hope the students will like this set and try to solve the numerical problems themselves.

1. A force of 1000 Newton is applied on a 25 kg mass for 5 seconds. What would be its velocity?

2. A force is applied on a mass of 16 kg for 3 seconds. As the force is removed the mass moves 81 meter in 3 seconds. What was the value of the force applied?

3. A mass of 50 kg was moving with a velocity 400 m/s. A force of 40000 N is applied on the mass and its velocity is reduced to 50 m/s after some time. What is the distance travelled by the mass during this period?

4. A ball of 150 g mass moves with 12 m/s and bounces back after hitting a wall with 20 m/s after a small duration of 0.01 second. What was the force applied on the ball when it hits the wall?

5. A force of 200 N is applied on a body and its velocity changes from 5m/s to 10m/s in a second. What is the mass of the body?

6. Momentum of an object changes from 100 kgm/s to 200 kgm/s in 2 seconds. What is the force applied on it?

7. A mass of 1 kg is moving from east to west with a velocity 10 m/s. A force is applied on it for 2 seconds and its velocity becomes 5 m/s. What is the value and direction of the force?

8. A truck of mass M is moved under a force F. If the truck is then loaded with an object equal to the mass of the truck and the driving force is halved, then how does the acceleration change?

9. Derive the unit of force using the second law of motion. A force of 5 N produces an acceleration of 8 ms-2 on a mass m1 and an acceleration of 24 m s–2 on a mass m2. What acceleration would the same force provide if both the masses are tied together?

10. Velocity versus time graph of a ball of mass 50 g rolling on a concrete floor is shown in Figure. Calculate the acceleration and frictional force of the floor on the ball.