A bullet of $$10\mathrm{g}$$ leaves the barrel of gun with a velocity of $$600\mathrm{m}/\mathrm{s}$$. If the barrel of gun is $$50\mathrm{cm}$$ long and mass of gun is $$3\mathrm{kg}$$, then value of impulse supplied to the gun will be :

An average force of $$125\mathrm{N}$$ is applied on a machine gun firing bullets each of mass $$10\mathrm{g}$$ at the speed of $$250\mathrm{m}/\mathrm{s}$$ to keep it in position. The number of bullets fired per second by the machine gun is :

A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. After collision, they stick together and continue to move together with velocity

The Young's modulus of a steel wire of length $$6\mathrm{m}$$ and cross-sectional area $$3{\mathrm{mm}}^2$$, is $$2\times 10^{11}\mathrm{N}/{\mathrm{m}}^2$$. The wire is suspended from its support on a given planet. A block of mass $$4\mathrm{kg}$$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $$\frac{1}{4}$$ of its value on the earth. The elongation of wire is (Take $$g$$ on the earth $$=10\mathrm{m}/{\mathrm{s}}^2$$) :

For a solid rod, the Young's modulus of elasticity is $3.2\times 10^{11}{\mathrm{Nm}}^{-2}$ and density is $8\times 10^3\mathrm{kg}{\mathrm{m}}^{-3}$. The velocity of longitudinal wave in the rod will be.

Under the same load, wire A having length $5.0\mathrm{m}$ and cross section $2.5\times 10^{-5}{\mathrm{m}}^2$ stretches uniformly by the same amount as another wire B of length $6.0\mathrm{m}$ and a cross section of $3.0\times 10^{-5}$ ${\mathrm{m}}^2$ stretches. The ratio of the Young's modulus of wire A to that of wire $B$ will be :

A mercury drop of radius $$10^{-3}\mathrm{m}$$ is broken into 125 equal size droplets. Surface tension of mercury is $$0.45{\mathrm{Nm}}^{-1}$$. The gain in surface energy is :

If 1000 droplets of water of surface tension $$0.07\mathrm{N}/\mathrm{m}$$, having same radius $$1\mathrm{mm}$$ each, combine to from a single drop. In the process the released surface energy is :- \left( {\mathrm{Take}\,\pi = {{22} \over 7}} \right)

A force is applied to a steel wire 'A', rigidly clamped at one end. As a result elongation in the wire is $0.2\mathrm{mm}$. If same force is applied to another steel wire ' $\mathrm{B}$ ' of double the length and a diameter $2.4$ times that of the wire ' $\mathrm{A}$ ', the elongation in the wire ' $\mathrm{B}$ ' will be (wires having uniform circular cross sections)

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, $$5\mathrm{cm}$$. If the tube is dipped in a similar manner in another liquid $$\mathrm{B}$$ of surface tension and density double the values of liquid $$\mathrm{A}$$, the height of liquid column raised in liquid $$\mathrm{B}$$ would be __________ m.

Choose the correct relationship between Poisson ratio $$(\sigma )$$, bulk modulus (K) and modulus of rigidity $$(\eta )$$ of a given solid object :

A fully loaded boeing aircraft has a mass of $$5.4\times 10^5$$ kg. Its total wing area is 500 m$${}^2$$. It is in level flight with a speed of 1080 km/h. If the density of air $$\rho$$ is 1.2 kg m$${}^{-3}$$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be. ($$\mathrm{g}=10m/{\mathrm{s}}^2$$)

Surface tension of a soap bubble is $$2.0\times 10^{-2}{\mathrm{Nm}}^{-1}$$. Work done to increase the radius of soap bubble from $$3.5\mathrm{cm}$$ to $$7\mathrm{cm}$$ will be: Take $$\left[\pi =\frac{22}{7}\right]$$

A bicycle tyre is filled with air having pressure of $$270\mathrm{kPa}$$ at $$27^{\circ }\mathrm{C}$$. The approximate pressure of the air in the tyre when the temperature increases to $$36^{\circ }\mathrm{C}$$ is

Match List I with List II .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} List I List II A. Surface tension I. $$\mathrm{kg}{\mathrm{m}}^{-1}{\mathrm{s}}^{-1}$$ B. Pressure II. $$\mathrm{kg}\mathrm{m}{\mathrm{s}}^{-1}$$ C. Viscosity III. $$\mathrm{kg}{\mathrm{m}}^{-1}{\mathrm{s}}^{-2}$$ D. Impulse IV. $$\mathrm{kg}{\mathrm{s}}^{-2}$$ Choose the correct answer from the options given below :

A bowl filled with very hot soup cools from 98$${}^{\circ }$$C to 86$${}^{\circ }$$C in 2 minutes when the room temperature is 22$${}^{\circ }$$C. How long it will take to cool from 75$${}^{\circ }$$C to 69$${}^{\circ }$$C?

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Steel is used in the construction of buildings and bridges. Reason R : Steel is more elastic and its elastic limit is high. In the light of above statements, choose the most appropriate answer from the options given below

The frequency ($$\nu$$) of an oscillating liquid drop may depend upon radius ($$r$$) of the drop, density ($$\rho$$) of liquid and the surface tension (s) of the liquid as $$\nu =r^a{\rho }^b{s}^c$$. The values of a, b and c respectively are

A 100 m long wire having cross-sectional area $$6.25\times 10^{-4}{\mathrm{m}}^2$$ and Young's modulus is $$10^{10}\mathrm{N}{\mathrm{m}}^{-2}$$ is subjected to a load of 250 N, then the elongation in the wire will be :

A wire of length ' $L$ ' and radius ' $r$ ' is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$, its length increases by ' $l$ '. Another wire of same material of length ' $2\mathrm{L}$ ' and radius ' $2 r$ ' is pulled by a force ' $2 f$ '. Then the increase in its length will be :