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qUESTIONS

Show that vectors a=2î+5ĵ-6k̂ and b̅ = î – 5/2ĵ – 3k̂ are parallel.

The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures and is initial velocity.

v= at + b/(t+c) + v0 is a dimensionally valid equation. Obtain the dimensional formula for a, b and c where v is velocity, t is time and v0

The diameter of a sphere is 2.14 cm. Calculate the volume of the sphere to the correct number of significant figures.

Write down the number of significant figures in the following: 0.003 m^2 , 0.1250 gm cm^-2, 6.4 x 10^6 m, 1.6 x 10^-19 C, 9.1 x 10^-31 kg.

If the formula for a physical quantity is X= (a^4x b^3)/(c^(1/3)d^(1/2)) and if the percentage error in the measurements of a, b, c and d are 2%, 3%, 3% and 4% respectively. Calculate percentage error in X.

When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be 35.72″ of arc. Calculate the diameter of the Jupiter.

If the length of a cylinder is l = (4.00±0.001) cm, radius r = (0.0250 ±0.001) cm and mass m = (6.25±0.01) gm. Calculate the percentage error in the determination of density.

An object is falling freely under the gravitational force. Its velocity after travelling a distance h is v. If v depends upon gravitational acceleration g and distance, prove with dimensional analysis that v = k gh where k is a constant.

In Ohm’s experiments, the values of the unknown resistances were found to be 6.12Ω, 6.09Ω, 6.22Ω,6.15Ω. Calculate the absolute error, relative error and percentage error in these measurements.

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