A new system of units is proposed in which unit of mass is `alpha` kg, unit of length `beta` m and unt of time `gamma`s. How much will 5 J measure in this new system?

A calorie is a unit of heat or energy and it equal about 4.2 J where 1J = 1 kg m^2 s^-2 . Suppose we employ a system of units in which the unit of mass equals alpha kg, the unit of length equals beta m, the unit of time is gamma s. Show that a calorie has a magnitude 4.2 alpha^-1 beta^-2 gamma^2 in terms of the new units.

If the unit of force is 100 N, unit of length is 10 m and unit of time is 100 s, what isw the unit of mass in this system of units?

An engine pumps out water continously through a hose with a veclocity v.If m is the mass per unit length of the water jet ,the rater at which the kinetic energy is imparted to water is :

The crystal system of a compound with unit cell dimensions alpha=0.387, b=0.387 and c=0.504 nm and alpha=beta=90^@ and gamma=120^@ is

A steel wire of mass mu per unit length with a circular cross section has a radius of 0.1 cm. The wire is of length 10 m when measured lying horizontal, and hangs from a hook on the wall. A mass of 25 kg is hung from the free end of the wire. Assuming the wire to be uniform and lateral strains < < longitudinal strains, find the extension in the length of the wire. The density of steel is 7860 kg m^-3 (Young's modulues Y = 2 xx 10^11 N m^-2)

If with reference to the right handed system of mutually perpendicular unit vectors hati, hatj, hatk , vec alpha = 3hati - hatj, vec beta = 2hati + hatj - 3hatk , then express vec beta in the form vec beta = vec beta_1 + vec beta_2 where vec beta_1 is parallel to vec alpha and vec beta_2 is perpendicular to vec alpha .

The principle of 'parallax' is used in the determination of distance of nearby stars. The role of distant object O there is now taken by nearby distant stars. The baseline AB is the line joining the Earth's two locations six months apart in its orbit around the Sun. That is the baseline is about the disameter of the earth's orbit = 3 xx 10^11 m. However, even the nearest stars are so distant that with such a long baseline theyshow parallax only of the order 1 s of arc or so. A parsec is a convenient unit of length on the astronomical sxale. It is the distance of an object that will show a parallar of 1s of arc from opposite ends of a baseline equal to the distance from the Earth to the Sum How much is a parsec in terms of metre?