A particle of mass m is projected vertically upwards from Earth’s surface with speed u. Earth has mass M and radius R. What is the minimum speed needed so the particle never returns?
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A particle of mass m is projected vertically upwards from Earth’s surface with speed u. Earth has mass M and radius R. What is the minimum speed needed so the particle never returns?

G1 Physics · Accepted Answer

Step 1: For the particle to just escape, the total mechanical energy at the launch point must be zero. Step 2: ½ μ \mu μ ²-GMm/R=0 gives u=√(2GM/R)=√(2gR). Final answer: A — √(2GM/R).