26224.The planet mercury is revolving in an elliptical orbit around the sun as shown in figure. The kinetic energy of mercury will be greater at
A
B
C
D
26225.Two planets of radii r1 and r2 are made from the same material. The ratio of the acceleration due to gravity g1/g2 at the surface of the two planets is
$\dfrac{r_{1}}{r_{2}}$
$\dfrac{r_{2}}{r_{1}}$
$\left(\dfrac{r_{1}}{r_{2}}\right)^{2}$
$\left(\dfrac{r_{2}}{r_{1}}\right)^{2}$
26226.A satellite is revolving around the sun in a circular orbit with uniform velocity v. If the gravitational force suddenly disappears, the velocity of the satellite will be
zero
v
2v
infinity
26227.Who among the following first gave the experimental velocity of G?
Cavendish
Copernicus
Brook Taylor
none of these
26228.The largest and the shortest distance of the earth from are r1 and r2. It’s distance from the sun when it is perpendicular to the major-axis of the orbit drawn from the sun.
$\left(\dfrac{r_{1}+r_{2}}{4}\right)$
$\left(\dfrac{r_{1}+r_{2}}{r_{1}-r_{2}}\right)$
$\left(\dfrac{2r_{1}r_{2}}{r_{1}+r_{2}}\right)$
$\left(\dfrac{r_{1}+r_{2}}{3}\right)$
26229.If R is radius of the earth and g the acceleration due to gravity on the earth’s surface, the mean density of the earth is
$\dfrac{4\pi G}{2gR}$
$\dfrac{3\pi G}{4gR}$
$\dfrac{3g}{4\pi RG}$
$\dfrac{4\pi RG}{3g}$
26230.The masses of two planets are in the ratio 1 : 2. Their radii are in the ratio 1 : 2. The acceleration due to gravity on the planets are in the ratio.
1 : 2
2 : 1
3 : 5
5 : 3
26231.When body is raised to a height equal to radius of earth, the P.E. change is
MgR
$\dfrac{MgR}{2}$
2 MgR
none of these
26232.A spherical planet far out in space has a mass M0 and diameter D0. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to
$\dfrac{GM_{0}}{D_{0}^{2}}$
$\dfrac{4mGM_{0}}{D_{0}^{2}}$
$\dfrac{4GM_{0}}{D_{0}^{2}}$
$\dfrac{GmM_{0}}{D_{0}^{2}}$
26233.If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would
decrease
remains unchanged
increase
none of these
26235.The escape velocity from the earth’s surface is 11 km/sec. A certain planet has a radius twice that of the earth but its mean density is the same as that of the earth. The value of the escape velocity from this planet would be
22 km/sec
11 km/sec
5.5 km/sec
16.5 km/sec
26236.If g is the acceleration due to gravity of the earth’s surface the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is
$\dfrac{1}{2}mgR$
2mgR
mgR
$\dfrac{1}{4}mgR$
26237.An earth’s satellite of mass m revolves in a circular orbit at a height h from the surface g is acceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by
$\dfrac{gR^{2}}{R+h}$
gR
$\dfrac{gR}{R+h}$
$\sqrt{\left(\dfrac{gR^{2}}{R+h}\right)}$
26238.The mean radius of the earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at earth’s surface is g. The cube of the radius of the orbit of a geo-stationary satellite will be
r2g/ ω
R2ω2 / g
RG ω2
R2g/ ω2
26239.The radii of the earth and the moon are in the ratio 10 : 1 while acceleration due to gravity on the earth’s surface and moon’s surface are in the ratio 6 : 1. The ratio of escape velocities from earth’s surface to that of moon surface is
10 : 1
6 : 1
1.66 : 1
7.74 : 1
26240.The escape velocity from earth is 11.2 km per sec. If a body is to be projected in a direction making an angle 45° to the vertical, then the escape velocity is
11.2 × 2 km/sec
11.2 km/sec
11.2 ×$\dfrac{1}{\sqrt{2}}$ km/sec
11.2 ×${\sqrt{2}}$ km/sec
26241.If the gravitational force between two objects were proportional to 1/R (and not as 1/R2) where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to
$\dfrac{1}{R^{2}}$
R0
R1
$\dfrac{1}{R}$
26242.What would be the duration of the year if the distance between the earth and the sun gets doubled?
1032 days
129 days
365 days
730 days
26243.If escape velocity from the earth’s surface is 11.2 km/sec. then escape velocity from a planet of mass same as that of earth but radius one fourth as that of earth is
11.2 km/sec
22.4 km/sec
5.65 km/sec
44.8 km/sec