Vidaara.orgClass 11 · Physics
CodeVID-P11-01-CH-01
Units and Measurements — Full Chapter Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Use the correct number of significant figures in every numerical answer.
- Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A (1 mark each)
6 × 1 = 6 marks
1.
The SI unit of amount of substance is the:
- A.kelvin
- B.mole
- C.candela
- D.kilogram
2.
The dimensional formula of power is:
- A.[M L^2 T^-2]
- B.[M L^2 T^-3]
- C.[M L T^-2]
- D.[M L^-1 T^-2]
3.
The number of significant figures in 2.0040 is:
- A.3
- B.4
- C.5
- D.6
4.
For Z = A × B, the relative error in Z equals:
- A.ΔA + ΔB
- B.ΔA/A + ΔB/B
- C.ΔA/A − ΔB/B
- D.ΔA · ΔB
5.
Which quantity has the same dimensions as pressure?
- A.energy density
- B.force
- C.power
- D.momentum
6.
A consistent one-directional error in every reading is called:
- A.random error
- B.systematic error
- C.least-count error
- D.no error
Section B (2 marks)
4 × 2 = 8 marks
7.
Convert 54 km/h into m/s.
8.
Write the dimensional formula of pressure and of energy.
9.
State the number of significant figures in 0.005080 and 1.2 × 10^3.
10.
Two lengths are (4.0 ± 0.1) cm and (3.0 ± 0.1) cm. Find their sum with error.
Section C (3 marks)
2 × 3 = 6 marks
11.
Check the dimensional consistency of v^2 = u^2 + 2as.
12.
A quantity P = a^2 b / c^3. The percentage errors in a, b, c are 1%, 2%, 1%. Find the maximum percentage error in P.
Section D (5 marks)
2 × 5 = 10 marks
13.
Using dimensional analysis, derive the time period of a simple pendulum assuming it depends on length l, mass m and acceleration due to gravity g. State one limitation of the method here.
14.
In an experiment to find g using g = 4π^2 l / T^2, length l = (100.0 ± 0.1) cm and time period T = (2.00 ± 0.01) s. Compute g and its percentage error.
Answer Key
Section A (1 mark each)
- (B) mole
- (B) [M L^2 T^-3]
- (C) 5
- (B) ΔA/A + ΔB/B
- (A) energy density
- (B) systematic error
Section B (2 marks)
- 15 m/s (54 × 5/18).
- Pressure [M^1 L^-1 T^-2]; energy [M^1 L^2 T^-2].
- 0.005080 has 4; 1.2 × 10^3 has 2.
- (7.0 ± 0.2) cm — absolute errors add.
Section C (3 marks)
- Every term has dimensions [L^2 T^-2], so the equation is dimensionally consistent.
- 2(1) + 2 + 3(1) = 7%.
Section D (5 marks)
- T = k √(l/g); independent of mass. Limitation: the constant k (= 2π) cannot be found by dimensions.
- g ≈ 9.87 m/s^2; %error = Δl/l + 2ΔT/T = 0.1% + 2(0.5%) = 1.1%.
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