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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 radii of the circular orbits of two satellites A and B of the earth are 4R and R, respectively. If the speed of the satellite A is 3v, then the speed of the satellite B will be:
A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 × 10²⁴ kg) have to be compressed to be a black hole?
A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest:
The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If $t_1$ is the time for planet to move from C to D and $t_2$ is the time to move from A to B, then:
The kinetic energies of a planet in an elliptical orbit around the Sun, at positions A, B and C are $K_A$, $K_B$ and $K_C$ respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S, as shown in the figure. Then:
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:
If the mass of the sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following statements would not be correct?
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 value $\gamma = \frac{C_P}{C_V}$ for hydrogen, helium, and another ideal diatomic gas $X$ (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to: