List of practice Questions

At what temperature is the R.M.S. velocity of a hydrogen molecule equal to that of an oxygen molecule at \(47^\circ\text{C}\)? (Molecular weight of hydrogen = 2, molecular weight of oxygen = 32)

Earth revolves round the sun in a circular orbit of radius \(R\). The angular momentum of the revolving earth is directly proportional to

If \(N\) is the number of turns in a circular coil, the value of its self-inductance varies as

From a uniform circular thin disc of mass \(9M\) and radius \(R\), a small disc of radius \(\frac{R}{3}\) is removed. The centre of the small disc is at a distance \(\frac{2R}{3}\) from the centre of the original disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the original disc is

A biconvex lens (\(R_1 = R_2 = 20\,\text{cm}\)) has focal length equal to the focal length of a concave mirror. The radius of curvature of the concave mirror is (\(\mu\) of glass lens = 1.5)

In the following network, \(I_1=-0.4\,\text{A}\), \(I_4=1\,\text{A}\) and \(I_5=0.4\,\text{A}\). The values of \(I_2\), \(I_3\) and \(I_6\) respectively are

When an electron in a hydrogen atom jumps from the third orbit to the second orbit, it emits a photon of wavelength \( \lambda \). When it jumps from the fourth orbit to the third orbit, the wavelength emitted by the photon will be

In Young’s double slit experiment, the 6th maximum with wavelength \( \lambda_1 \) is at a distance \( d_1 \) from the central maximum and the 4th maximum with wavelength \( \lambda_2 \) is at distance \( d_2 \). Then \( \dfrac{d_1}{d_2} \) is

If \(E\), \(M\), \(L\) and \(G\) denote energy, mass, angular momentum and constant of gravitation respectively, then the quantity \( \left(\dfrac{EL^2}{G^2M^5}\right) \) has dimensions of

A circular coil of radius \(R\) carries an electric current \(I\). The magnetic field due to the coil at a point on the axis of the coil located at a distance \(r\) from the centre of the coil, such that \(r \gg R\), the magnetic field at that point is proportional to

A glass slab of thickness \(4\,\text{cm}\) contains the same number of waves as in \(x\,\text{cm}\) of water column when both are traversed by the same monochromatic light. If the refractive indices of glass and water for that light are \( \frac{5}{3} \) and \( \frac{4}{3} \) respectively, the value of \(x\) will be

A toroidal solenoid with air core has an average radius \(R\), number of turns \(N\) and area of cross-section \(A\). The self-inductance of the solenoid is (Neglect the field variation across the cross-section of the toroid)

The length of a potentiometer wire is \(L\). A cell of e.m.f. \(E\) is balanced at a length \( \frac{L}{5} \) from the positive end of the wire. If the length of the wire is increased by \( \frac{L}{2} \), at what distance will the same cell give a balance point?

\( \vec{A} \) and \( \vec{B} \) are two non-zero vectors inclined at an angle \( \theta \). \( \hat{a} \) and \( \hat{b} \) are unit vectors along \( \vec{A} \) and \( \vec{B} \) respectively. The component of \( \vec{A} \) in the direction of \( \vec{B} \) is

An electron accelerated through potential difference \(V\) passes through a uniform transverse magnetic field and experiences a force \(F\). If the accelerating potential is increased to \(2V\), the electron in the same magnetic field will experience a force

Binding energy of a revolving satellite at height \(h\) is \(3.5\times10^8\,\text{J}\). Its potential energy is

Two springs of spring constants \(K\) and \(2K\) are stretched by the same force. If \(W_1\) and \(W_2\) are the energies stored in them respectively, then

A particle performs S.H.M. with amplitude \( A \). Its speed is tripled at the instant when it is at a distance of \( \frac{2A}{3} \) from the mean position. The new amplitude of the motion is

A Fraunhofer diffraction pattern due to a single slit of width \(0.3\,\text{mm}\) is obtained on a screen placed at a distance of \(3\,\text{m}\) from the slit. The first minima lie at \(5.5\,\text{mm}\) on either side of the central maximum on the screen. The wavelength of light used is

One end of thick horizontal copper wire of length \(2L\) and radius \(2R\) is welded to the end of another thin horizontal copper wire of length \(L\) and radius \(R\). When they are stretched by applying the same force at the two ends, the ratio of the elongation in the thick wire to that in the thin wire is

The non-zero potential difference across diode \(D_1\) and that across diode \(D_2\) are equal in the circuit shown in the figure (both diodes are identical in characteristics)

If \( \vec{A} = 3\hat{i} - 2\hat{j} + \hat{k} \), \( \vec{B} = \hat{i} - 3\hat{j} + 5\hat{k} \) and \( \vec{C} = 2\hat{i} + \hat{j} - 4\hat{k} \) form a right angled triangle, then out of the following which one is satisfied?

A donor impurity results in

A mass \( m \) is tied to one end of a spring and whirled in a horizontal circle with constant angular velocity. The elongation in the spring is 1 cm. If the angular speed is doubled, the elongation in the spring is 6 cm. The original length of the spring is

If \[ A = \begin{bmatrix} 1 & 3 \\ 2 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix}, \] then \[ B^{-1} A^{-1} = \]