Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
99 Percentile Qs Bank for JEE MainPhysicsGravitation

A planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at points (A ) and (B ) are (90 10^6 ~km ) and (60 10^6 ~km ), respectively. The ratio of velocities of the planet at the points (A ) and (B ) when its velocities make angle (30^ ) and (60^ ) with major-axis of the orbit is

Options

  1. A( 3 2 3 )
  2. B( 2 3 )
  3. C( 1 3 )
  4. D( 3 2 )

Correct answer

B. ( 2 3 )

Step-by-step solution

According to the law of conservation of angular momentum, angular momentum ((J) ) of a planet is constant. ( aligned & m u_A r_A _A=m u_B r_B _B & or u_A v_B = r_B r_A _B _ A & Given, r_A=90 10^6 ~km , r_B=60 10^6 ~km & _A=30^ , _B=60^ aligned ) ( aligned or u_A u_B & = 60 10^6 90 10^6 60^ 30^ & = 2 3 3 / 2 1 / 2 or u_A u_B & = 2 3 aligned ) Hence, the ratio of velocities of the planet is (2 3 ).

Practice Gravitation on Quantrex Academy →

More from Gravitation

A particle of mass m , and angular momentum is moving in a circular orbit of radius r₀ under the influence of an attractive force F (r) = - k r^2 r . Keeping its angular momentum u 2026A body of mass m is taken from the surface of earth to a height equal to twice the radius of earth ( R_e ). The increase in potential energy will be _______. ( g is acceleration du 2026When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface. The change in g is approximately %. The value of is _____. (Take radius of t 2026The height in terms of radius of the earth (R) , at which the acceleration due to gravity becomes g 9 , where g is acceleration due to gravity on earth's surface, is ______. 2026If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy (k) on reaching the surface of earth. The values of v and k respectively are ___ 2026A planet (P₁) is moving around the star of mass 2M in the orbit of radius R . Another planet (P₂) is moving around another star of mass 4M in a orbit of radius 2R . Ratio of time p 2026Three masses 200 ~kg , 300 ~kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 2026Given below are two statements: Statement I : A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends up 2026 Full Gravitation list All 99 Percentile Qs Bank for JEE Main PYQs