A projectile of mass $M$ is fired so that the horizontal range is $4\, km$. At the highest point the projectile explodes in two parts of masses $M/4$ and $3M/4$ respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is .................. $\mathrm{km}$
A projectile of mass $M$ is fired so that the horizontal range is $4\, km$. At the highest point the projectile explodes in two parts of masses $M/4$ and $3M/4$ respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is .................. $\mathrm{km}$
- [JEE MAIN 2013]
- A
$16$
- B
$1$
- C
$10$
- D
$2$
Similar Questions
An isolated rail car of mass $M$ is moving along a straight, frictionless track at an initial speed $v_0$. The car is passing under a bridge when $a$ crate filled with $N$ bowling balls, each of mass $m$, is dropped from the bridge into the bed of the rail car. The crate splits open and the bowling balls bounce around inside the rail car, but none of them fall out. Is the momentum of the rail car $+$ bowling balls system conserved in this collision?
An isolated rail car of mass $M$ is moving along a straight, frictionless track at an initial speed $v_0$. The car is passing under a bridge when $a$ crate filled with $N$ bowling balls, each of mass $m$, is dropped from the bridge into the bed of the rail car. The crate splits open and the bowling balls bounce around inside the rail car, but none of them fall out. Is the momentum of the rail car $+$ bowling balls system conserved in this collision?
A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy $K$ with time $t$ most appropriately? The figures are only illustrative and not to the scale.
A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy $K$ with time $t$ most appropriately? The figures are only illustrative and not to the scale.
- [IIT 2014]
A particle of mass $m$ travelling along $x-$ axis with speed $v_0$ shoots out $1/3^{rd}$ of its mass with a speed $2v_0$ along $y-$ axis. The velocity of remaining piece is
A particle of mass $m$ travelling along $x-$ axis with speed $v_0$ shoots out $1/3^{rd}$ of its mass with a speed $2v_0$ along $y-$ axis. The velocity of remaining piece is
A particle is moving along a vertical circle of radius $R$. At $P$, what will be the velocity of particle (assume critical condition at $C)$ ?
A particle is moving along a vertical circle of radius $R$. At $P$, what will be the velocity of particle (assume critical condition at $C)$ ?
Two incitned frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track. Will the stones reach the bottom at the same time? Will they reach there with the same speed? Explain. Given $\theta_{1}=30^{\circ}, \theta_{2}=60^{\circ},$ and $h=10\; m ,$ what are the speeds and times taken by the two stones?
Two incitned frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track. Will the stones reach the bottom at the same time? Will they reach there with the same speed? Explain. Given $\theta_{1}=30^{\circ}, \theta_{2}=60^{\circ},$ and $h=10\; m ,$ what are the speeds and times taken by the two stones?