A bullet of mass $m$ moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a height $h$, the initial velocity of the bullet will be
A bullet of mass $m$ moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a height $h$, the initial velocity of the bullet will be
- A
$\frac{{m + M}}{m}\sqrt {2gh} $
- B
$\sqrt {2gh} $
- C
$\frac{{M + m}}{M}\sqrt {2gh} $
- D
$\frac{m}{{M + m}}\sqrt {2gh} $
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In an elastic collision of two particles the following quantity is conserved
In an elastic collision of two particles the following quantity is conserved
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 ?
Two identical $5\,\,kg.$ blocks are moving with same speed of $2\,\,m/s$ towards each other along a frictionless horizontal surface. The two blocks collide, stick together and come to rest. Consider to two blocks as a system, the work done on the system by the external forces will be .............. $\mathrm{Joule}$
Two identical $5\,\,kg.$ blocks are moving with same speed of $2\,\,m/s$ towards each other along a frictionless horizontal surface. The two blocks collide, stick together and come to rest. Consider to two blocks as a system, the work done on the system by the external forces will be .............. $\mathrm{Joule}$
A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time $t^{\prime}$ is proportional to :
A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time $t^{\prime}$ is proportional to :
The length of a spring is $\alpha $ when a force of $4\,N$ is applied on it and the length is $\beta $ when $5\,N$ force is applied. Then the length of spring when $9\,N$ force is applied is
The length of a spring is $\alpha $ when a force of $4\,N$ is applied on it and the length is $\beta $ when $5\,N$ force is applied. Then the length of spring when $9\,N$ force is applied is