A shell of mass $m$ moving with velocity $v$ suddenly breakes into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be
A shell of mass $m$ moving with velocity $v$ suddenly breakes into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be
- A
$v$
- B
$\frac{5v}{4}$
- C
$\frac{4v}{5}$
- D
$\frac{v}{5}$
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Answer the following :
$(a)$ The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere?
$(b)$ Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet’s velocity in general. Yet the work done by the gravitational force over every complete orbit of the comet is zero. Why ?
$(c)$ An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, however small. Why then does its speed increase progressively as it comes closer and closer to the earth ?
$(d)$ In Figure $(i)$ the man walks $2\; m$ carrying a mass of $15\; kg$ on his hands. In Figure $(ii)$, he walks the same distance pulling the rope behind him. The rope goes over a pulley, and a mass of $15\; kg$ hangs at its other end. In which case is the work done greater ?
Answer the following :
$(a)$ The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere?
$(b)$ Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet’s velocity in general. Yet the work done by the gravitational force over every complete orbit of the comet is zero. Why ?
$(c)$ An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, however small. Why then does its speed increase progressively as it comes closer and closer to the earth ?
$(d)$ In Figure $(i)$ the man walks $2\; m$ carrying a mass of $15\; kg$ on his hands. In Figure $(ii)$, he walks the same distance pulling the rope behind him. The rope goes over a pulley, and a mass of $15\; kg$ hangs at its other end. In which case is the work done greater ?
The work done by a force $\vec F\, = \,( - \,6{x^3}\,\hat i)N$ , in displacing a particle from $x = 4\,m$ to $x = -\,2\,m$ is .............. $\mathrm{J}$
The work done by a force $\vec F\, = \,( - \,6{x^3}\,\hat i)N$ , in displacing a particle from $x = 4\,m$ to $x = -\,2\,m$ is .............. $\mathrm{J}$
The force acting on a body moving along $x-$ axis varies with the position of the particle as shown in the figure. The body is in stable equilibrium at
The force acting on a body moving along $x-$ axis varies with the position of the particle as shown in the figure. The body is in stable equilibrium at
Figure shows the vertical section of frictionless surface. $A$ block of mass $2\, kg$ is released from the position $A$ ; its $KE$ as it reaches the position $C$ is ................ $\mathrm{J}$
Figure shows the vertical section of frictionless surface. $A$ block of mass $2\, kg$ is released from the position $A$ ; its $KE$ as it reaches the position $C$ is ................ $\mathrm{J}$
After on head on elastic collision between two balls of equal masses , one is observed to have a speed of $3\, m/s$ along positive $x$ -axis and the other has a speed of $2\, m/s$ along negative $x$ -axis. The original velocities of the balls are
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