Latest Posts

A wire of density 9 × 10–3 kg cm–3 is stretched between two clamps 1 m apart. The resulting strain in the wire is 4.9 × 10–4. The lowest frequency of the transverse vibrations in the wire is (Young’s modulus of wire Y = 9 ×1010 Nm–2), (to the nearest integer), _______.

Answer: (35) \(\begin{array}{l}f=\frac{1}{2l}\sqrt{\frac{T}{\mu }}=\frac{1}{2l}\sqrt{\frac{T}{\rho A}}=\frac{1}{2l}\sqrt{\frac{Y\Delta l}{\rho l}}\end{array} \) \(\begin{array}{l}f=\frac{1}{2\times 1}\sqrt{\frac{9\times 10^{10}\times 4.9\times 10^{-4}}{9000\times 1}}=35 Hz\end{array} \)

a particle of mass m is moving along the x axis with initial velocity it collides elastically with a particle of mass 10 m at rest and then moves with half its initial kinetic energy

Answer: (10) \(\begin{array}{l}\frac{1}{2}mv_{1}^{2}=\frac{1}{2}\left ( \frac{1}{2}mu^{2} \right )\end{array} \), \(\begin{array}{l}v_{1}^{2}=u^{2}/2\end{array} \), \(\begin{array}{l}v_{1}=u/\sqrt{2}\end{array} \)——–(i) Also, \(\begin{array}{l}\frac{1}{2}mu^{2}=\frac{1}{2}mv_{1}^{2}+\frac{1}{2}\times 10m\times v_{2}^{2}\end{array} \), \(\begin{array}{l}\frac{1}{2}\times 10m\times v_{2}^{2}=\frac{1}{2}\times... View Article

A square shaped hole of side l =a/2 is carved out at a distance d = a/2 from the centre ‘O’ of a uniform circular disk of radius a. If the distance of the centre of mass of the remaining portion from O is– a/X, value of X (to the nearest integer) is _________.

Answer: (23) \(\begin{array}{l}X_{cm}=\frac{\pi a^{2}\times 0-\frac{a^{2}}{4}\times \frac{a}{2}}{\pi a^{2}-\frac{a^{2}}{4}}\end{array} \) \(\begin{array}{l}X_{cm}=\frac{-a}{2(4\pi -1)}=\frac{-a}{8\pi -2}\end{array} \) X= (8 π-2) = 8 x 3.14 -2... View Article

The height ‘h’ at which the weight of a body will be the same as that at the same depth ‘h’ from the surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected):

1) \(\begin{array}{l}\frac{\sqrt{3}R-R}{2}\end{array} \) 2) \(\begin{array}{l}\frac{\sqrt{5}}{2}R-R\end{array} \) 3) \(\begin{array}{l}\frac{\sqrt{5}R-R}{2}\end{array} \) 4) \(\begin{array}{l}\frac{R}{2}\end{array} \) Answer: (3) \(\begin{array}{l}\frac{g_{0}}{(1+\frac{h}{R})^{2}}=g_{0}\left [ 1-\frac{h}{R} \right ]\end{array} \)... View Article

A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 Nm–1, density = 667 kg m–3) which rises to height h in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60° with one another. Then h is close to (g=10 ms–2).

1) 0.172 m 2) 0.049 m 3) 0.087 m 4) 0.137 m Answer: (3) \(\begin{array}{l}h=\frac{2Tcos\theta }{\rho gr}\left \{ \theta =30^{0}... View Article