1: A pulley of radius 0.9 m is used to left the bucket from the well. If it took 3.6 rotation for the pulley to take water out of the well, how deep is the water in the well.

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2: The length of a pendulum is (1.5 ± 0.01) m and the acceleration due to gravity is taken into account as (9.8 + 0.1) ms⁻². Calculate the time period of the pendulum with uncertainty in it. (2.5 ± 0.8 %) 




3: Determine the area of a rectangular sheet with length (I ± Δl) = (1.50 ± 0.02) m and width (w ± Δw) = (0.20 ± 0.01) m. Calculate the area (A + ΔA). (0.30 m², ± 0.02 m²)

4: Calculate the answer up to appropriate numbers of significant digits 

(a) 246.24 + 238.278 + 98.3 

(b) 1.4 x 2.639 + 117.25 

(c) (2.66 x 10⁴) - (1.03 x10³) 

(d) (112 x 0.456) / (3.2 x 120) 

(e) 168.99 x 9 

(f) 1023 + 8.5489 

Ans [(a) 582.8 , (b) 120.9, (c) 2.56 x 10⁴, (d) 0.13 , (e) 2000 & (f) 1032 ]

5: Calculate the answer up to appropriate numbers of significant digits 

(a) The ratio of mass of proton 'mₚ' to the mass of electron 'mₑ' 

`\frac {mₚ}{mₑ}` = `\frac {1.67 x 10⁻²⁷ kg}{9.1096 x 10⁻³¹ kg}`

(b) The ratio of charge on electron 'qₑ' to mass of electron 'mₑ' 

`\frac {qₑ}{mₑ}` = `\frac {1.6 x 10⁻¹⁹ C}{9.1096 x 10⁻³¹ kg}`

6: Find the dimensions of 

(a) planck's constant 'h' from formula E = hf Where E is the energy and f is frequency. 

(b) gravitational constant 'G' from the formula F = G `frac {m₁m₂}{r^2}`. Where 'F' is force, 'm₁' and 'm₂' are masses of objects and 'r' is the distance between centers of objects. 

(a) [ML²T⁻¹] (b)[M⁻¹L³T⁻²]




7: Show that 

(a) KE = `\frac {1}{2}` mv²

and 

(b) PE𝖌 = mgh 

are dimensionally correct. 

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