A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 4R. The ratio of their respective periods is
1) 4 : 1 2) 1 : 8 3) 8 : 1 4) 1 : 4 5) 1 : 2... View Article
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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
1) decrease 2) remain unchanged 3) increase 4) be zero Answer: 3) increase Solution: The acceleration due to gravity is given... View Article
The escape velocity from the earth is 11 kms -1. The escape velocity from a planet having twice the radius and same mean density as that of earth is
1) 5.5 kms -1 2) 11 kms -1 3) 22 kms -1 4) None of these Answer: 3) 22 kms -1 Solution:... View Article
A body is projected with a velocity of 2 × 11.2 km/s from the surface of earth. The velocity of the body when it escapes the gravitational pull of the earth is
1) √3 × 11.2 km/s 2) 11.2 km/s 3) √2 × 11.2 km/s 4) 0.5 × 11.2 km/s 5) 2... View Article
Two bodies of masses m and 4m are placed at a distance of r. The gravitational potential at a point on the line joining them where the gravitational field is zero is
1) – 4Gm/r 2) -6Gm/r 3) -9Gm/r 4) zero Answer: 3) -9Gm/r Solution: Let A and B be the two masses... View Article
The acceleration due to gravity becomes (g/2) at a height equal to (g = acceleration due to gravity on the surface of the earth)
1) 4R 2) R/4 3) 2R 4) R/2 Answer: 2) R/4 Solution: The acceleration due to gravity g=GM/R2 At a height... View Article
If the diameter of mass is 6760 km and mass one-tenth that of the earth. The diameter of the earth is 12742 km. If acceleration due to gravity on earth is 9.8 ms -2, the acceleration due to gravity on mass is
1) 34.8 ms -2 2) 2.48 ms -2 3) 3.48 ms -2 4) 28.4 ms -2 Answer: 3) 3.48 ms -2 Solution:... View Article
Two balls, each of radius R, equal mass and density are placed in contact, then the force of gravitation between them is proportional to
1) \(\begin{array}{l}F\propto \frac{1}{R^{2}}\end{array} \) 2) \(\begin{array}{l}F\propto R\end{array} \) 3) \(\begin{array}{l}F\propto R^{4}\end{array} \) 4) \(\begin{array}{l}F\propto \frac{1}{R}\end{array} \) Answer: 3) \(\begin{array}{l}F\propto R^{4}\end{array} \) Solution: Distance between their centres... View Article
Two spherical bodies of mass M and 5 M and radii R and 2 R, respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before the collision is
1) 2.5 R 2) 4.5 R 3) 7.5 R 4) 1.5 R Answer: 3) 7.5 R Solution: The gravitational force, \(\begin{array}{l}F(x)=\frac{GM5M}{(12R-x)^{2}}\end{array} \)... View Article
Two particles of equal mass m go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to their centre of
1) \(\begin{array}{l}\sqrt{\frac{Gm}{R}}\end{array} \) 2) \(\begin{array}{l}\sqrt{\frac{Gm}{4R}}\end{array} \) 3) \(\begin{array}{l}\sqrt{\frac{Gm}{3R}}\end{array} \) 4) \(\begin{array}{l}\sqrt{\frac{Gm}{2R}}\end{array} \) Answer: 2) \(\begin{array}{l}\sqrt{\frac{Gm}{4R}}\end{array} \) Solution: \(\begin{array}{l}\frac{Gm^{2}}{(2R)^{2}}=m\omega^{2}R\end{array} \) \(\begin{array}{l}\frac{Gm^{2}}{4R^{3}}= \omega^{2}\end{array} \) \(\begin{array}{l}\omega=\sqrt{\frac{Gm}{4R^{3}}}\end{array} \)... View Article
If g is the acceleration due to gravity on 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
1) (1/2) mg R 2) 2 mg R 3) mg R 4) (1/4) mg R Answer: 1) (1/2) mg R Solution:... View Article
In a satellite, if the time of revolution is T, then KE is proportional to
1) 1/T 2) 1/T2 3) 1/T3 4) T-2/3 Answer: Time period T ∝ r3/2 r ∝ T2/3 and kinetic energy 1/r ∝... View Article
A body weighs 500 N on the surface of the earth. How much would it weigh half-way below the surface of the earth?
1) 125 N 2) 250 N 3) 500 N 4) 1000 N Answer: 2) 250 N Weight (W) of a... View Article
If the radius of earth is R, then the height h at which the value of g becomes one-fourth, will be
1) R/8 2) 3R/8 3) 3R/4 4) R/2 Answer: 2) 3R/8 Solution: Let g be the acceleration due to gravity then... View Article
If g is the acceleration due to gravity on the surface of the earth, its value at a height equal to double the radius of the earth is
1) g 2) g/2 3) g/3 4) g/9 Answer: Acceleration due to gravity at a height h from the surface... View Article
At what depth below the surface of the earth, the value of g is the same as that at a height of 5 km?
1) 1.25 km 2) 2.5 km 3) 5 km 4) 7.5 km 5) 10 km Answer: 3) 10 km Solution: Variation... View Article
A gas is undergoing a change in state by an isothermal process AB as follow. Work done by gas in process AB is
a. 100 ln2 Joule b. −100 ln2 Joule c. 200 ln2 Joule d. −200 ln2 Joule Solution: Answer: (c) Wisothermal... View Article
If N0 active nuclei become N0/16 in 80 days. Find half-life of nuclei?
a. 40 days b. 20 days c. 60 days d. 30 days Solution: Answer: (b)
Two stars of masses m1 and m2 are in mutual interaction and revolving in orbits of radii r1 and r2 respectively. The time period of revolution for this system will be?
a. \(\begin{array}{l}2\pi \sqrt{\frac{(r_{1}-r_{2})^{3}}{G(m_{1}+m_{2})}}\end{array} \) b. \(\begin{array}{l}2\pi \sqrt{\frac{(r_{1}+r_{2})^{3}}{G(m_{1}+m_{2})}}\end{array} \) c. \(\begin{array}{l}2\pi \sqrt{\frac{(r_{1}-r_{2})^{3}}{G(m_{1}-m_{2})}}\end{array} \) d. \(\begin{array}{l}2\pi \sqrt{\frac{(r_{1}+r_{2})^{3}}{G(m_{1}-m_{2})}}\end{array} \) Solution: Answer: (b) Let... View Article
Find the value of Rp in the given circuit? (VZ = 8V)
a. 4Ω b. 6Ω c. 3Ω d. 5Ω Solution: Answer: (b) Applying KVL 20 – 8 – 2RP = 0... View Article
