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A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of the bullet before hitting the wood is 10 m s$$^{-1}$$ and, it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is $$x$$ N. The value of $$x$$ to the nearest integer is ________.
Correct Answer: 10
We are given a bullet of mass $$m = 0.1 \text{ kg}$$ with initial velocity $$u = 10 \text{ m/s}$$ that comes to rest ($$v = 0$$) after penetrating a distance $$s = 50 \text{ cm} = 0.5 \text{ m}$$ into a wooden block with uniform deceleration.
Using the kinematic equation $$v^2 = u^2 + 2as$$, we get $$0 = (10)^2 + 2a(0.5)$$, which gives $$a = -\dfrac{100}{1} = -100 \text{ m/s}^2$$.
The magnitude of the retarding force is $$F = ma = 0.1 \times 100 = 10 \text{ N}$$.
The answer is $$\boxed{10}$$.
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