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The approximate depth of an ocean is $2700 \text{ m}$. The compressibility of water is $45.4 \times 10^{-11} \text{ Pa}^{-1}$ and the density of water is $10^3 \text{ kg/m}^3$. What fractional compression of water will be obtained at the bottom of the ocean?
At what height from the surface of earth the gravitation potential and the value of g are -5.4 × 10^7 J kg^-1 and 6.0 m s^-2 respectively? (Take the radius of earth as 6400 km.)
The velocity of a small ball of mass $M$ and density $d$, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $d/2$, then the viscous force acting on the ball will be:
Match List- I with List- II. List-I (Measured values) (A) 0.001213 (B) $2.1 \times 10^{16}$ (C) 3.70 (D) 3000 List-II (Significant figures) (I) 2 (II) 3 (III) 1 (IV) 4
A body weighs 200 N on the surface of the earth. How much will it weigh half way down to the centre of the earth ?
A bullet from a gun is fired on a rectangular wooden block with velocity $u$. When the bullet travels $24\text{ cm}$ through the block along its length horizontally, velocity of bullet becomes $u/3$. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:
A particle of mass m is thrown upwards from the surface of the earth with a velocity u. The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth is
A planet moving along an elliptical orbit is closest to the sun at a distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are the linear velocities at these points respectively, then the ratio v₁/v₂ is:
The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R₁ to another of radius R₂ (R₂ > R₁) is
The dimensions $[MLT^{-2}A^{-2}]$ belong to the:
At constant temperature, on increasing the pressure of a gas by 5%, its volume will decrease by:
At what temperature is the root mean square velocity of gaseous hydrogen molecules equal to that of oxygen molecules at 47°C?
Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? (g=10 m/s²)
The molecules of a given mass of gas have RMS velocity of $200 \text{ ms}^{-1}$ at $27^\circ\text{C}$ and $1.0 \times 10^5 \text{ Nm}^{-2}$ pressure. When the temperature and the pressure of the gas are respectively, $127^\circ\text{C}$ and $0.05 \times 10^5 \text{ Nm}^{-2}$, the RMS velocity of its molecules in $\text{ms}^{-1}$ is:
The ratio of the specific heats $C_P/C_V = \gamma$ in terms of degrees of freedom ($n$) is given by:
If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is
Two sound waves with wavelengths $5.0 \text{ m}$ and $5.5 \text{ m}$, respectively, propagate in a gas with a velocity of $330 \text{ m/s}$. How many beats per second can we expect?
Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic), the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement, among the following, is:
At any instant of time $t$, the displacement of any particle is given by $2t-1$ (SI unit) under the influence of the force of $5\text{ N}$. The value of instantaneous power (in SI units) is:
The temperature at which the RMS speed of atoms in neon gas is equal to the RMS speed of hydrogen molecules at $15^\circ\text{C}$ is: (the atomic mass of neon $= 20.2 \text{ u}$, molecular mass of hydrogen $= 2 \text{ u}$)