Q. 67

Expert-verifiedFound in: Page 356

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

Two Jupiter-size planets are released from rest 1.0 x 10^{11 }m apart. What are their speeds as they crash together?

Speed at crashing of planet is 4.35 x 10^{4} m/s

The distance between the two planets at rest is 1.0 x 10^{11} m.

The mass of the planet is 1.90 x 10^{27} kg

the mean radius of the planet is 6.99 x 10^{7} m

From the law of conservation of energy,

K_{1} + U_{1} = K_{2} + U_{2} ..............................................(1)

K_{1} is the kinetic energy of the planets before collision.U_{1} is the potential energy of planets before collision.K_{2} is the kinetic energy of the planets after collision.U_{2} is the potential energy of the planets after collision.

Calculate the initial kinetic energy of the planets usingm = mass of planets.v_{1} = initial velocity of the planets.As planets are initially at rest so their initial kinetic energy is zero.K_{1} =0

Initial potential energy (due to gravitational force) is

G = gravitational constant.r1 = initial distance between the two planets.

Similarly find the final kinetic energy

and final potential energy

Substitute these in the equation (1) and solve for velocity

Now substitute values and calculate velocity

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