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# Class XI Physics Unit, Dimensions and Errors 3

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Question 1

When a small sphere moves at low speed through a fluid, the viscous force F, opposing the motion is experimentally found to depend upon the radius r, the velocity of the sphere and the η viscosity of the fluid. The expression for force will be

Question 2

A gas bubble from an explosion under water, oscillates with a period T proportional to pa db Ec where p is the static pressure, d is the density of water and E is the total energy of explosion. Find the values of a, b and c.

Question 3

A quantity X is given by ,where ε0 is the permittivity of the free space, L is a length, ΔV is a potential difference and Δt is a time interval. The dimensional formula for X is the same as that of

Question 4

A cube has a side of length 1.2 × 10–2m. Calculate its volume.

Question 5

The velocity v of surface waves on a liquid may be related to their wavelength λ, the surface tension of liquid σ and its density ρ by the following equation: v = where k is a dimensionless constant. The values of α, β and γ should respectively be given as

Question 6

The density of a sphere is measured by measuring its mass and diameter. If it is known that the maximum percentage errors in the measurement are 2% and 3%, then find the maximum percentage error in the measurement of density?

Question 7

Which of the following set have different dimensions?

Question 8

A formula is given as ,where P = pressure, k = Boltzmann’s constant, θ = temperature, t = time, a and b are constants. Dimensional formula of b is same as
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