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Question

Ratio of minimum kinetic energies of two projectiles of same mass is 4:1. The ratio of the maximum height attained by them is also 4:1. The ratio of their ranges would be


Your Answer
A
16:1
Correct Answer
B
4:1
Your Answer
C
8:1
Your Answer
D
2:1

Solution

The correct option is B 4:1
Velocity of a projectile motion is minimum at the highest point of the trajectory
Thus, vmin=u cosθ   
Minimum kinetic of the projectile =  K.E=12m(ucosθ)2
According to question, K.E1K.E2=12mu21cos2θ112mu22cos2θ2=41(1)
Let H1 and H2 be the maximum heights of two projectiles. We are given that H1H2=41
u21sin2θ12gu22sin2θ22g=41(2)
Also, we know that R=u2sin2θg=2u2sinθcosθg 
R21R22=u41sin2θ1cos2θ1u42sin2θ2cos2θ
Multiplying (1) and (2), we get
u41sin2θ1cos2θ1u41sin2θ2cos2θ2=161R21R22=161R1R2=41

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