A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of 100 m from the foot of the tower. A body of mass 2 M thrown at a velocity v/2 from the top of the tower of height 4 H will touch the ground at a distance of _______.

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JEE Mains · Physics · STD 11 - Motion in plane

JEE Mains 2024
Hard
Numerical

A body of mass \(M\) thrown horizontally with velocity \(v\) from the top of the tower of height \(\mathrm{H}\) touches the ground at a distance of \(100 \mathrm{~m}\) from the foot of the tower. A body of mass \(2 \mathrm{M}\) thrown at a velocity \(\frac{v}{2}\) from the top of the tower of height \(4 \mathrm{H}\) will touch the ground at a distance of _______.

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Verified Solution

Answer & Solution

Correct Answer

(A) \(100\)

Step-by-step Solution

Detailed explanation

\(100=v \sqrt{\frac{2 \mathrm{H}}{\mathrm{g}}} ; \quad \mathrm{x}=\frac{v}{2} \sqrt{\frac{2(4 \mathrm{H})}{\mathrm{g}}}=v \sqrt{\frac{2 \mathrm{H}}{\mathrm{g}}}\)

\(\Rightarrow \mathrm{x}=100\)

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