Exams › JEE Advanced › Physics

Two particles of masses m and M start from rest, separated by a very large distance, and are drawn together by their mutual gravitational attraction. When their separation has reduced to d, what is the speed of one particle relative to the other?

1. sqrt(G*(M + m)/(2*d))
2. sqrt(G*(M + m)/d)
3. sqrt(4*G*(M + m)/d)
4. sqrt(2*G*(M + m)/d)

Correct answer: sqrt(2*G*(M + m)/d)

Solution

Energy conservation: the PE released going from infinity to separation d is G*M*m/d, which equals total KE. With momentum conservation, m*v1 = M*v2, and relative speed v_rel = v1 + v2. The KE = (1/2)*mu*v_rel² where mu = mM/(M+m) is the reduced mass. So G*M*m/d = (1/2)*(mM/(M+m))*v_rel². Solving: v_rel² = 2*G*(M+m)/d, so v_rel = sqrt(2*G*(M+m)/d).

Related JEE Advanced Physics questions

• Rain is falling at an angle α with respect to the vertical at a velocity of 10 m/s. A girl runs in the opposite direction to the rain at a speed of 8 m/s and observes that the rain appears to make an angle β with the vertical. What is the relationship between α and β?
• A vector A is turned by a very small angle Δθ radians (where Δθ is much less than 1) to form a new vector B. What is the magnitude of the difference |B − A|?
• A swimmer moves through water at a speed of v relative to the water. To cross a river of width d, which flows at a speed u (where u < v), the downstream displacement caused by the river's flow is x. Which of the following is accurate?
• A particle is launched from a point with an initial speed u at an angle θ above the horizontal. At a specific point during its motion, its velocity becomes perpendicular to its original direction. What is the time taken to reach this point?
• A particle of mass m is projected form the ground with an initial speed u₀ at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u₀. The angle that the composite system makes with the horizontal immediately after the collision is
• A projectile is launched from level ground with an initial velocity v at an angle θ to the horizontal. The range of the projectile is initially d when the gravitational acceleration is g. If, at the peak of its motion, the projectile enters a zone where the effective gravitational acceleration becomes g' = g/0.81, the new range becomes d'. What is the value of n?

⚔️ Practice JEE Advanced Physics free + battle 1v1 →