A ball is dropped from height $10 \,m$. Ball is embedded in sand $1 \,m$ and stops, then

  • A

    Only momentum remains conserved

  • B

    Only kinetic energy remains conserved

  • C

    Both momentum and K.E. are conserved

  • D

    Neither K.E. nor momentum is conserved

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A projectile is moving at $20\,m/sec$ at its highest point where it breaks into two equal parts due to an internal explosion. One part moves vertically up at $30\,m/sec$ . Then the other part will move at ............. $\mathrm{m}/ \mathrm{s}$

The potential energy function for a particle executing linear simple harmonic motion is given by $V(x)=$ $k x^{2} / 2,$ where $k$ is the force constant of the oscillator. For $k=0.5\; N m ^{-1}$ the graph of $V(x)$ versus $x$ is shown in Figure. Show that a particle of total energy $1 \;J$ moving under this potential must 'turn back" when it reaches $x=\pm 2 m$

A projectile is fired at a speed of $100\, m/sec$ at an angle of $37^o$ above the horizontal. At the highest point, the projectile breaks into two parts of mass ratio $1:3$ , the smaller coming to rest. Then the distance of heavier part from the launching point is ............... $\mathrm{m}$

In a system of particles, internal forces can change (for the system)

In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls ? (i.e. when they are in contact)

$(a)$ Kinetic energy.

$(b)$ Total linear momentum.

Give reason for your answer in each case.