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:

• A. 16 : 1
• B. 4 : 1
• C. 8 : 1
• D. 2 : 1S

Answer 1

Answer: (B)

4 : 1

Answer 2

$\frac { \frac { 1 } { 2 } m u _ { 1 } ^ { 2 } \cos ^ { 2 } \theta _ { 1 } } { \frac { 1 } { 2 } m u _ { 2 } ^ { 2 } \cos ^ { 2 } \theta _ { 2 } } = \frac { 4 } { 1 }$

̃ $\frac { u _ { 1 } \cos \theta _ { 1 } } { u _ { 2 } \cos \theta _ { 2 } } = 2$ …(1)

And $\frac { u _ { 1 } ^ { 2 } \sin ^ { 2 } \theta _ { 1 } } { u _ { 2 } ^ { 2 } \sin ^ { 2 } \theta _ { 2 } } = \frac { 4 } { 1 }$

or $\frac { \mathrm { u } _ { 1 } \sin \theta _ { 1 } } { \mathrm { u } _ { 2 } \sin \theta _ { 2 } } = \frac { 2 } { 1 }$ …(2)

from equation no. (1) and (2)

$\frac { \mathrm { u } _ { 1 } \sin \theta _ { 1 } \cdot \mathrm { u } _ { 1 } \cos \theta _ { 1 } } { \mathrm { u } _ { 2 } \sin \theta _ { 2 } \cdot \mathrm { u } _ { 2 } \cos \theta _ { 2 } } = \frac { 4 } { 1 }$

$\frac { \mathrm { gR } _ { 1 } / 2 } { \mathrm { gR } _ { 2 } / 2 } = \frac { 4 } { 1 }$ ̃ $\frac { \mathrm { R } _ { 1 } } { \mathrm { R } _ { 2 } } = \frac { 4 } { 1 }$