Question Bank Directory

Which of the following system of units is not based on units of mass, length and time alone?

A physical quantity of the dimensions of length that can be formed out of $c$, $G$ and $\frac{e^2}{4\pi\varepsilon_0}$ is [$c$ is the velocity of light, $G$ is the universal constant of gravitation and $e$ is charge]

If dimensions of critical velocity $v_c$ of a liquid flowing through a tube are expressed as $[\eta^x \rho^y r^z]$, where $\eta$, $\rho$ and $r$ are the coefficient of viscosity of the liquid, the density of liquid and radius of the tube respectively, then the values of $x$, $y$ and $z$ are given by

Dimensional formula $ML^2T^{-3}$ represents

The dimension of $\frac{1}{2}\varepsilon_0 E^2$, where $\varepsilon_0$ is permittivity of free space and $E$ is electric field, is

If force $[F]$, acceleration $[A]$ and time $[T]$ are chosen as the fundamental physical quantities, then find the dimensions of energy:

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 percentage errors in the measurement of mass and momentum of an object are 1% and 2% respectively. The percentage error in the measurement of kinetic energy of the object will be:

When the circular scale of a screw gauge completes 2 rotations, it covers 1 mm over the pitch scale. The total number of circular scale divisions is 50. The least count of the screw gauge in metres is:

A metal wire has mass $(0.4\pm 0.002)\text{ g}$, radius $(0.3\pm 0.001)\text{ mm}$ and length $(5\pm 0.02)\text{ cm}$. The maximum possible percentage error in the measurement of density will nearly be:

If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{E}{G}$ has the dimensions of:

For a p-type semiconductor, which of the following statements is true ?

The unit of thermal conductivity is :

A block of mass $m$ is moving with initial velocity $u$ towards a stationary spring of stiffness constant $k$ attached to the wall as shown in the figure. Maximum compression of the spring is: (The friction between the block and the surface is negligible).

Let $T_1$ and $T_2$ be the energy of an electron in the first and second excited states of hydrogen atoms, respectively. According to the Bohr's model of an atom, the ratio $T_1 : T_2$ is

A mass $m$ slips along the wall of a semispherical surface of radius $R$. The velocity at the bottom of the surface is:

Two bodies $A$ and $B$ of the same mass undergo completely inelastic one-dimensional collision. The body $A$ moves with velocity $v_1$ while the body $B$ is at rest before collision. The velocity of the system after collision is $v_2$. The ratio of $v_1 : v_2$ is:

The object $A$ has half the kinetic energy as that of the object $B$. The object $B$ has half the mass as that of the object $A$. The object $A$ speeds up by $1\text{ ms}^{-1}$ and then has the same kinetic energy as that of the object $B$. The initial speed of the object $A$ is: (Take $\sqrt{2} \cong 1.4$)

A stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is:

A man pushes a wall and fails to displace it. He does: