JEE Main · 2005 · 08 May 2005 · Offline · Work, Power & Energy

WhatsApp Email

A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

(A)3.0 cm
(B)2.0 cm
(C)1.5 cm
(D)1.0 cm✓ Correct

Answer: (D)

Solution

Let the target apply a constant resisting force

F

. Losing half the speed in the first

3

cm means, by the work-energy theorem,

F \cdot 3 = \frac{1}{2} m v^{2} - \frac{1}{2} m (\frac{v}{2})^{2} = \frac{3}{8} m v^{2}

. To stop completely from

v

the force must absorb all the kinetic energy,

F (3 + x) = \frac{1}{2} m v^{2}

. Dividing the two relations,

\frac{3 + x}{3} = \frac{1/2}{3/8} = \frac{4}{3}

, so

3 + x = 4

and the bullet penetrates a further

x = 1

cm.

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

Practise more: all JEE Main PYQs on Work, Power & Energy →

More JEE Main questions on Work, Power & Energy

Given below are two statements:
Statement I: An object moves from position $r_{1}$ to position $r_{2}$ under a conservative force field $F$ . The work done by the force is $W = - \int_{r_{1}}^{r_{2}} F \cdot d r$ .
Statement II: Any object moving from one l …
JEE Main 2026View solution →
Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$ . Their centers have an initial separation of $4 R$ . Both the spheres are given an initial speed of $u$ towards each other. The minimum value of $u$ , so that they can just touch e …
JEE Main 2026View solution →
A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $x (t) = α t^{2} + β t + γ m$ , where $α = 1 m / s^{2}$ , $β = 1 m / s$ an …
JEE Main 2026View solution →
In case of vertical circular motion of a particle by a thread of length r if the tension in the thread is zero at an angle 30° shown in figure, the velocity at the bottom point (A) of the circular path is (g = gravitational acceleration)
JEE Main 2026View solution →
A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is $____$ N.
JEE Main 2026View solution →
A 1 kg block subjected to two simultaneous forces $(2 \hat{i} + 3 \hat{j} + 4 \hat{k})$ N and $(3 \hat{i} - \hat{j} - 2 \hat{k})$ N is moved a distance of 25 m along $(3 \hat{i} - 4 \hat{j})$ direction. The work done in this process is _____ J.
JEE Main 2026View solution →