Asked: R.O./A.R.O. (Pre) Exam. 2017medium Level
QUESTION STATEMENT:द्विभाषी / Bilingual
दो समान द्रव्यमान की वस्तुओं की गतिज ऊर्जाओं का अनुपात 4:9 है, तो उनके वेगों का अनुपात होगा -
The kinetic energies of two objects of equal mass are in the ratio 4:9. The ratio of their velocities will be -
SELECT CORRECT OPTION:
A
$4 : 9$
B
Correct$2 : 3$
C
$16 : 81$
D
$\sqrt{2} : \sqrt{3}$
Official Solution & Explanation:
Correct Answer: Option B($2 : 3$)
गतिज ऊर्जा $K = \frac{1}{2}mv^2$। समान द्रव्यमान के लिए: $\frac{K_1}{K_2} = \frac{v_1^2}{v_2^2} = \frac{4}{9} \implies \frac{v_1}{v_2} = \sqrt{\frac{4}{9}} = \frac{2}{3}$ अर्थात $2 : 3$।
Kinetic energy is given by $K = \frac{1}{2}mv^2$. For equal masses, $\frac{K_1}{K_2} = \left(\frac{v_1}{v_2}\right)^2 = \frac{4}{9} \implies \frac{v_1}{v_2} = \frac{2}{3}$.