Units and Measurement

A physical quantity X is given by X =  The percentage error in the measurement of k, l,  m  and n are 1 %, 2%, 3% and 4% respectively. The value of X is uncertain by

• 8%

• 10%

• 12%

• None of these

If the units of length, mass and force are chosen as fundamental units, the dimensions of time would be

• [ M^1/2 L^-1/2 F^1/2 ]

• [ M^1/2 L^1/2 F^1/2 ]

• [ M^1/2 L^1/2 F^-1/2 ]

• [ M^1/2 L^-1/2 F^-1/2 ]

If an error in measurement of radius of a sphere is 1%, what will be the error in the measurement of volume?

• 1 %

• 1.3 %

• 3 %

• 10 %

If C and R denote capacity and resistance, the dimensions of C R are :

• M⁰L⁰T

• ML⁰T

• M⁰L⁰T²

• not expressible in terms of M, L and T

The length, breadth and thickness of a block are given by l = 12 cm, b = 6 cm and t = 2.45 cm. The volume of the block according to the idea of significant figures should be:

• 1 × 10² cm³

• 2 × 10² cm³

• 1.763 × 10² cm³

• none of the above

The dimensional formula for Young's modulus is

• [ML^-1T^-2]

• [M⁰LT^-2]

• [MLT^-2]

• [ML²T^-2]

Dimensions of torque is

• [M¹L²T^-2]

• [M²L²T²]

• [M^-1LT^-1]

• [M^-2L^-2T^-2]

If x = $\frac{{\mathrm{\epsilon }}_0 \mathrm{lV}}{\mathrm{t}}$is the permittivity of free space, l is length, V is potential difference and t is time. The dimensions of x are same as that of

• charge

• resistance

• voltage

• current

Dimension of $\frac{\mathrm{L}}{\mathrm{RCV}}$ is

• [A^-1]

• [A^-2]

• [A]

• [A²]

The length, breath and thickness of a block are given by l = 12 cm, b= 6 cm and t = 2.45 cm. The volume of the  block according to the idea of significant figure should be

• 1 x 10² cm²

• 2 x 10² cm³

• 1.763 x 10² cm²

• None of these