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(A) $1$. Kinetic energy $E_k$ at height $h$ is given by $E_k = E_{total} - mgh$. This is a linear equation of the form $y = mx + c$ with a negative sl

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$3$ only

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(A) $1$. Kinetic energy $E_k$ at height $h$ is given by $E_k = E_{total} - mgh$. This is a linear equation of the form $y = mx + c$ with a negative slope,so the graph of $E_k$ vs $h$ should be a straight line with a negative slope. Figure $1$ shows a curve,which is incorrect.$2$. Height $h$ at time $t$ is given by $h = ut - \frac{1}{2}gt^2$. This is a quadratic equation representing a parabola opening downwards. Figure $2$ shows a straight line,which is incorrect.$3$. Gravitational potential energy $E_g$ at height $h$ is given by $E_g = mgh$. This is a linear equation of the form $y = mx$ with a positive slope. Figure $3$ shows a straight line passing through the origin,which is correct.Therefore,only statement $3$ is correct.

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$A$ simple pendulum of length $1 \ m$ has a bob of mass $1 \ kg$. $A$ bullet of mass $10^{-2} \ kg$ is fired into the bob with a speed of $2 \times 10^2 \ m/s$. The bullet gets embedded in the bob. Find the height $h$ to which the bob rises before it swings back. (in $m$)

Statement $-1$: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Statement $-2$: Principle of conservation of momentum holds true for all kinds of collisions.

In a one-dimensional collision between two particles,their relative velocity is $\vec{v}_1$ before the collision and $\vec{v}_2$ after the collision.

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