CBSE Class 11 Physics Units Dimensions Vectors Advanced Problems

1. Find the dimension of
(a) electric field E
(b) magnetic field B
(c) magnetic permeability μ0.
The relevant equations are F = q E, F = qv B, and B =μ0I/2∏α, where F is force, q is charge, v isspeed, I is current, and α is distance.

2. Find the dimension of
(a) electric dipole moment p
(b) magnetic dipole moment M. The defining equations are p = q.d. and M = IA , where d is distance, A is area, q is charge and I is current.

3. Find the dimensions of
(a) the specific heat capacity c
(b) the coefficient of linear expansion α and
(c) the gas constant R.
Some of the equations involving these quantities are Q = mc (T₂ – T₁), lt = l0 [1 + α (T₂ – T₁)] and PV = nRT.

4. Taking force, length and time to be the fundamental quantities find the dimensions of
(a) density (b) pressure
(c) momentum (d) energy
5. Let x and a stand for distance. Is òd x/ √a² – x² = 1/a  sin^–1 a/x dimensionally correct ?

6. A carrom board (4 ft × 4 ft square) has the queen at the centre. The queen, hit by the striker moves to the front edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen
(a) from the centre to the front edge,
(b) from the front edge to the hole
(c) from the centre to the hole.

7. Refer to the figure. Find
(a) the magnitude,
(b) x and y components and
(c) the angle with the X-axis of the resultant of OA, BC and DE .

8. If a and b are two vectors, then what will be the value of (a + b) × (a – b).

9. A particle moves on a given straight line with a constant speed v. At a certain time it is at a point P on its straight line path. O is a fixed point. Show that OP vr × is independent of the position P.

10. Find the unit vector along the vector A × B. Where A = 2i + 3j and B = i + j.

11. The electric current in a charging R–C circuit is given by i = i₀ e^–t/RC where i₀, R and C are constant parameters of the circuit and t is time. Find the rate of change of current at (a) t = 0, (b) t = RC, (c) t = 10 RC.

12. A rod of length L is placed along the X-axis between x = 0 and x = L. The linear density (mass/length) ρ of the rod varies with the distance x from the origin as ρ = a + bx. (a) Find the SI units of a and b. (b) Find the mass of the rod in terms of a, b and L.

13. The momentum p of a particle changes with time t according to the relationd dp/dt = (10 N) + (2 N/s) t.If the momentum is zero at t = 0 what will the momentum be at t = 10 s ?

14. Do you think that commutative and associtave laws are valid for vector subtraction also?, if yes write down the correct mathematical form and prove them, if no explain why not?

15. It it possible to have the modulus of subtraction of two vectors greater than the modulus of addition of the same two vectors.

16. Will it be possible to have the modulus of subtraction of two vectors less than the subtraction of the modulus of the same two vectors.

17. A particle is moving eastward with a velocity 10 m/s. In 10 s the velocity changes to 10 m/s northwards. Find the average acceleration during this time.

18. A body goes 20 km north and then 10 km due east. Find the displacement of body from its starting point.

19. Position of a particle is given as x = 3t + 5 where x in meter and t in seconds. Find velocity (dx/dt) of particle at time t = 5 second.

Advanced Level Assignment
1. (a) MLT^–3 A  (b) MT^–2 A^–1 (c) MLT^–2 A^–2  2. (a) LTA (b) L²A  3. (a) L2 T–2 K^–1 (b) K^–1 (c) ML² T^–2 K^–1 (mol)^–1 4. (a) FL^–4 T² (b) FL^–2 (c) FT (d) FL   5. No 6. (a)  2/3 √10 ft (b) 4/3 √10 ft (c) 2 √2 ft  7. (a) 1.6m (b) 0.98 m and 1.3 m (c) tan^–1 (1.32) 8. 2(b × a) 10. k 11. (a)  i₀ /RC(b) i₀ /RCe (c) i₀ /RCe¹⁰  12. (a) kg/m, kg/m² (b) aL +bL²/2 13. 200 kg-m/s 14. No, 15. Yes 16. Yes 17. √2 ms^–2 N-W 18. 22.36 km 19. 3 m/s