NEET Dimensions Practice Questions With Solutions

A balloon is made of a material of surface tension \(S\) and its inflation outlet (from where gas is filled in it) has small area \(A.\) It is filled with a gas of density \(\rho\) and takes a spherical shape of radius \(R.\) When the gas is allowed to flow freely out of it, its radius \(r\) changes from \(R\) to \(0\) (zero) in time \(T.\) If the speed \(v(r)\) of gas coming out of the balloon depends on \(r\) as \(r^a\) and \(T \propto S^\alpha A^\beta \rho^\gamma R^\delta\) then:

A force defined by; \(F = \alpha t^2 + \beta t\) acts on a particle at a given time \(t.\) The factor which is dimensionless, if \(\alpha\) and \(\beta\) are constants, is:

The quantities which have the same dimensions as those of solid angle are:

The mechanical quantity, which has dimensions of reciprocal of mass \((M^{-1}),\) is:

Plane angle and solid angle have:

The dimensions \([MLT^{-2}A^{-2}]\) belong to the:

The physical quantity that has the same dimensional formula as pressure is:

If \(E\) and \(G\) respectively, denote energy and gravitational constant, then \(\dfrac{E}{G}\) has the dimensions of: