Question:
The force constant of a spring gun is $50 \,N / m$. If a ball of $20 \,g$ be shoot by the gun, so that its spring is compressed by $10 \,cm$, the velocity of the ball is:
The force constant of a spring gun is $50 \,N / m$. If a ball of $20 \,g$ be shoot by the gun, so that its spring is compressed by $10 \,cm$, the velocity of the ball is:
Updated On: Aug 15, 2022
- 5 m/s
- 15 m/s
- 25 m/s
- 20 m/s
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The Correct Option is A
Solution and Explanation
$\frac{1}{2} mv ^{2}=\frac{1}{2} kx ^{2}$
$v =\sqrt{\frac{ R }{ m }} x$
$=\sqrt{\frac{50}{20 \times 10^{-3}}}\left(10 \times 10^{-2}\right)$
$=50 \times 10^{-1}$
$=5 \,m / s$
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Concepts Used:
Gravitation
In mechanics, the universal force of attraction acting between all matter is known as Gravity, also called gravitation, . It is the weakest known force in nature.
Newton’s Law of Gravitation
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
- F ∝ (M1M2) . . . . (1)
- (F ∝ 1/r2) . . . . (2)
On combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2
The dimension formula of G is [M-1L3T-2].