A particle of mass m is fired at speed of V 0 from a distance of 5 R from the center of a planet of mass M and radius R- Particle is fired at angle of - as shown in figure- For what value of - -in degree- will particle just graze the planet- Here V 0- GM -5 R and M - m Write upto two digits after the

By conservation of energy nbsp; ⇒ GMm/5R+1/2mV_0^2= GMm/R+1/2mV^2 By conservation of angular momentum, nbsp;mV_0 sinθ× 5R=mVR Solving both we get θ=37^∘ ...

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A particle of mass m is fired at speed of $V_{0}$ from a distance of 5R from the center of a planet of mass M and radius R. Particle is fired at angle of $θ$ as shown in figure. For what value of $θ$ [in degree] will particle just graze the planet. Here $V_{0} = \sqrt{\frac{G M}{5 R}}$ and M >> m (Write upto two digits after the decimal point.)

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Solution

By conservation of energy $\Rightarrow \frac{- G M m}{5 R} + \frac{1}{2} m V_{0}^{2} = \frac{- G M m}{R} + \frac{1}{2} m V^{2}$

By conservation of angular momentum,
$m V_{0} sin θ \times 5 R = m V R$

Solving both we get $θ = 37^{\circ}$

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By conservation of energy ⇒−GMm5R+12mV20=−GMmR+12mV2 By conservation of angular momentum, mV0sinθ×5R=mVR Solving both we get θ=37∘

By conservation of energy $\Rightarrow \frac{- G M m}{5 R} + \frac{1}{2} m V_{0}^{2} = \frac{- G M m}{R} + \frac{1}{2} m V^{2}$

By conservation of angular momentum,
$m V_{0} sin θ \times 5 R = m V R$

Solving both we get $θ = 37^{\circ}$