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A satellite is revolving in a circular orbit at a height h from the earth surface, such that h << R where R is the radius of the earth. Assuming that the effect of earth’s atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is:

a. \(\begin{array}{l}\sqrt{gR}\end{array} \) b. \(\begin{array}{l}\sqrt{2gR}\end{array} \) c. \(\begin{array}{l}\sqrt{gR}(\sqrt{2}-1)\end{array} \) d. \(\begin{array}{l}\sqrt{\frac{gR}{2}}\end{array} \) Answer: (c) \(\begin{array}{l}v_{0}=\sqrt{g(R+h)}\approx \sqrt{gR}\end{array} \) \(\begin{array}{l}v_{e}=\sqrt{2g(R+h)}\approx \sqrt{2gR}\end{array} \)... View Article

An equilateral triangle ABC is cut from a thin solid sheet of wood. (see figure) D, E and F are the mid-points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I0. It the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. Then:

a. \(\begin{array}{l}I=\frac{9}{16}I_{0}\end{array} \) b. \(\begin{array}{l}I=\frac{3}{4}I_{0}\end{array} \) c. \(\begin{array}{l}I=\frac{1}{4}I_{0}\end{array} \) d. \(\begin{array}{l}I=\frac{15}{4}I_{0}\end{array} \) Answer: (d) Suppose M is mass and a... View Article

A slab is subjected to two forces [latex]vec{F_{1}}[/latex] and [latex]vec{F_{2}}[/latex] of same magnitude F as shown in the figure. Force [latex]vec{F_{2}}[/latex]is in XY-plane while force F1 acts along z-axis at the point [latex](2vec{i}+3vec{j})[/latex]. The moment of these forces about point O will be:

a. \(\begin{array}{l}(3\hat{i}-2\hat{j}-3\hat{k})F\end{array} \) b. \(\begin{array}{l}(3\hat{i}+2\hat{j}+3\hat{k})F\end{array} \) c. \(\begin{array}{l}(3\hat{i}+2\hat{j}-3\hat{k})F\end{array} \) d. \(\begin{array}{l}(3\hat{i}-2\hat{j}+3\hat{k})F\end{array} \) Answer: (d) Torque for F1 force \(\begin{array}{l}\vec{F_{1}}=\frac{F}{2}(-\hat{i})+\frac{F\sqrt{3}}{2}(-\hat{j})\end{array} \)... View Article

A liquid of density [latex]rho[/latex] is coming out of a hose pipe of radius a with horizontal speed v and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be:

a. \(\begin{array}{l}\rho v^{2}\end{array} \) b. \(\begin{array}{l}\frac{3}{4}\rho v^{2}\end{array} \) c. \(\begin{array}{l}\frac{1}{2}\rho v^{2}\end{array} \) d. \(\begin{array}{l}\frac{1}{4}\rho v^{2}\end{array} \) Answer: (b) Momentum per... View Article

The force of interaction between two atoms is given by [latex]F = alpha beta expleft [ frac{-x^{2}}{alpha kt} right ][/latex]; where x is the distance, k is the Boltzmann constant and T is temperature [latex]alpha[/latex] and [latex]beta[/latex] are two constants. The dimension of [latex]beta[/latex] is:

a. M2L2T–2 b. M2LT–4 c. M0L2T–4 d. MLT–2 Answer: (b) \(\begin{array}{l}F=\alpha \beta e^{\frac{-x^{2}}{\alpha KT}}\end{array} \) \(\begin{array}{l}\left [ \frac{x^{2}}{\alpha KT} \right... View Article

Black Sea

The Black Sea is a large inland sea situated at the southeastern extremity of Europe. It is one of the... View Article