A projectile thrown with a speed v at an angle θ has a range R on the surf

Question

A projectile thrown with a speed v at an angle

θ

has a range R on the surface of earth. For same v and

θ

, its range on the surface of moon will be

Options:

A . R6

B . 6R

C . R36

D . 36R

Answer: Option B
:
B

R = \frac{u^{2} s i n 2 θ}{g} ∴ R \propto \frac{1}{g} \frac{R_{M o o n}}{R_{E a r t h}} = \frac{g_{E a r t h}}{g_{M o o n}} = 6 [∵ g_{M o o n} = \frac{1}{6} g_{E a r t h}] ∴ R_{M o o n} = 6 R_{E a r t h} = 6 R

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