CBSE Class 11 Physics Units Dimensions Vectors Basic Problems

1. The value of acceleration due to gravity is 980 cm/s². Find its value if the unit of length is kilometre and that of time is minute using method of dimensional equation.

2. It is given that the time period of oscillation, T, of a gas bubble from an explosion under water depends upon pressure, p, density of water, d, and total energy of explosion, E, as T ∝ p^a d^b E^c . Derive a relation for T in terms of various dimensions (powers) of p, d and E.

3. Assuming that the mass M of the largest stone that can be moved by a flowing river depends upon the velocity v of water, acceleration due to gravity g and density d of water. Find the dependence of M on velocity v using dimensional equation.

4. It is experimentally observed that the frequency f of a tuning fork depends upon the length l of the prongs of the tuning fork and density d and Young’s modulus Y of its material. Derive a relation for the frequency of tuning fork in terms of l, d and Y using principle of homogeneity of dimensions.

5. A planet moves around the sun in a circular orbit. The time period of revolution t of the planet depends upon radius of orbit R, mass of sun M and Gravitational constant G. Derive a relation for t in terms of R, M and G using dimensional equation.

6. Find the scalar product and angle between the vectors A = i + j –2k and B = –i + 2j – k

7. A particle suffers three displacements by 4m northwards, 2m in south-east direction and 1m in southwest direction. Find the displacement of the particle and distance covered by it.

8. A force F = 5i – 3j + 2k Newton is applied to a particle so that it moves from a distance r₁ = 2i + 7j + 4k m to r₂ = –5i + 2j + 3k m. Find the work done.

9. If vectors A = 3i –2j + k, B = i – 3j + 5k and c = 2i + j – 4k form a triangle. Find
(a) Which two vectors combine to form the third vector as their resultant ?
(b) Which vectors are perpendicular to each other.

10. Find the unit vector which is perpendicular to each of the vectors A = 3i + j + 2k and B = 2i –2j + 4k . Also find the sine of angle between vectors A and B.

11. Find the angle between vectors A = i –5j and B = 2i – 10j

12. Find the area of a parallelogram formed from the vectors A = (i – 2j + 3k)m and B = (3i –2j + k)m which are the adjacent sides of the parallelogram.

13. Find the derivative of the following functions with respect to x:
(a) ax + b (b) sin(x2) (c) sin2(x2) (d) log (ax + b) (e) xsin x (f) ex sinx