Internal Force

Q. A shell at rest on a smooth horizontal surface explodes into two fragments of masses $m_1$ and $m_2$. If just after explosion $m_1$ move with speed $u$, then work done by internal forces during explosion is

1. $\frac{1}{2}(m_1+m_2)\frac{m_2}{m_1}{u}^2$
2. $\frac{1}{2}(m_2+m_1)u^2$
3. $\frac{1}{2}{m}_1{u}^2(1+\frac{m_1}{m_2})$
4. $\frac{1}{2}(m_2-m_1)u^2$

Q. In the given diagram a $0.1\text{kg}$ bullet moving with speed $20\text{m/s}$ strikes the $1.9\text{kg}$ mass resting on a smooth block and gets embedded in it. Find the kinetic energy of the mass with which it will strike the ground.

1. $21\text{J}$
2. $18\text{J}$
3. $25\text{J}$
4. $12\text{J}$

Q. A rectangular plate of mass $20\text{kg}$ is suspended from points A and B as known, if the pin B is suddenly removed, the angular acceleration in ${\text{rad/s}}^2$(to the nearest integer) of the plate is $\alpha$.
Then $\frac{\alpha }{8}$ has value $(g=10{\text{m/s}}^2$)

Q. A stationary body explodes into four identical fragments such that three of them fly off mutually perpendicular to each other, each with same KE, $E_0$. The energy of explosion will be:

1. $6E_0$
2. $\frac{4E_0}{3}$
3. $4E_0$
4. $8E_0$

Q. A shell at rest on a smooth horizontal surface explodes into two fragments of masses $m_1$ and $m_2$. If just after explosion $m_1$ move with speed $u$, then work done by internal forces during explosion is

1. $\frac{1}{2}(m_1+m_2)\frac{m_2}{m_1}{u}^2$
2. $\frac{1}{2}(m_2+m_1)u^2$
3. $\frac{1}{2}{m}_1{u}^2(1+\frac{m_1}{m_2})$
4. $\frac{1}{2}(m_2-m_1)u^2$

Q. Theory of relativity reveals that mass can be converted into energy . The energy E so obtained is proportional to certain power of mass M and the speed C of light guess a relation among the qunantities using the method of dimensions

Q.

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 Fig. 6.13(i) the man walks 2 m carrying a mass of 15 kg on his hands. In Fig. 6.13(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?

Fig. 6.13

Q. A body of mass $8m$ is kept in $X-Y$ plane at rest. If it suddenly explodes into three pieces with two of them moving perpendicular to each other at equal speeds, the kinetic energy generated during explosion is (refer figure)

1. $m{v}^2$
2. $\frac{m{v}^2}{2}$
3. $\frac{5m{v}^2}{6}$
4. $\frac{7m{v}^2}{6}$

Q. A bomb burst in three fragments in which two fragments of equal mass of $1kg$ each moving with speed $v$ right angle to each other while third fragment of having mass twice that of either masses. If kinetic energy of system (all masses) increase by $96J$ after bursting then find out CORRECT statement about third fragment:

1. Will move with speed $4m/s$ at angle of ${135}^o$ to either.
2. Will move with speed $4\sqrt{2}m/s$ at angle of ${135}^o$ to either.
3. Will move with speed $4\sqrt{2}m/s$ at angle of ${45}^o$ to either.
4. Will move with speed $4m/s$ at angle of ${45}^o$ to either.

Q. An explosion blows a rock into three pieces. Two pieces go off at right angles to each other. One piece of these two has mass $1kg$ and moves with velocity $12m/s$ ; other has mass $2kg$ and moves with velocity $8m/s$. If the velocity of the third piece is $40$ m/sec, then its mass is.

1. $5kg$
2. $0.25kg$
3. $0.75kg$
4. $0.5kg$

Q. Two bodies in space start moving towards each other, due to the gravitational force between them. Which of the following is true for these two bodies, assuming there are no other forces acting on them?

1. The total energy is constant throughout this process
2. Energy is maximum when the distance between them is maximum
3. Internal energy decreases with time
4. The total kinetic energy increases with time

Q. A stationary body explodes into two fragments of masses $m_1$ and $m_2$. If momentum of one fragments p, the minimum energy of explosion is

1. $\frac{p^2}{2(m_1+m_2)}$
2. $\frac{p^2}{2\sqrt{m_1{m}_2}}$
3. $\frac{p^2}{2(m_1-m_2)}$
4. $\frac{p^2(m_1+m_2)}{4m_1{m}_2}$

Q. A mass of $1kg$ is thrown up with velocity of $1000m/s$.After $5$ second , it explodes into two parts. One part of mass $400g$ moves soen with a velocity $25m/s$ calculate the velocity of other part just after the explosion $(g=10m{s}^{-2})$

Q. a particle is projected vertically upward from the surface of earth with a kinetic energy equal to one fourth of the minimum value needed for it to escape the height to which it

Q. A bomb is kept stationary at a point. It suddenly explodes into two fragments of masses $1g$ and $3g$. The total kinetic energy of the fragments is $6.4\times {10}^{4}J$. What is the kinetic energy of the smaller fragment?

1. $9.6\times {10}^{4}J$
2. $2.5\times {10}^{4}J$
3. $3.5\times {10}^{4}J$
4. $5.2\times {10}^{4}J$

Q. A shell at rest on a smooth horizontal surface explodes into two fragments of masses $m_1$ and $m_2$. If just after explosion $m_1$ move with speed $u$, then work done by internal forces during explosion is

1. $\frac{1}{2}(m_1+m_2)\frac{m_2}{m_1}{u}^2$
2. $\frac{1}{2}(m_2+m_1)u^2$
3. $\frac{1}{2}{m}_1{u}^2(1+\frac{m_1}{m_2})$
4. $\frac{1}{2}(m_2-m_1)u^2$

Q. A particle of mass 4m which is at rest explodes into three fragments. Two of the fragments, each of mass m are found to move with speed v each, in mutually perpendicular directions. The total energy released in the process of explosion is-

1. $\left(\frac{2}{3}\right)m{v}^2$
2. $\left(\frac{3}{2}\right)m{v}^2$
3. $\left(\frac{4}{3}\right)m{v}^2$
4. $\left(\frac{3}{4}\right)m{v}^2$

Q. A body of mass 10 kg at rest explodes into two pieces of masses 7 kg and 3 kg. If the total Increase in kinetic energy due to explosion is 1680 J, the magnitude of their relative velocity in m/s, after explosion is

1. $40$
2. $50$
3. $70$
4. $80$

Q. Why is energy released when binding energy increases?

Q. A stationary body explodes into three fragments of masses $m_1$, $m_2$ and $m_3$. If the momentum of one fragment is p and one fragment of mass $m_3$ remains at rest, the energy of explosion is:

1. $\frac{p^2}{2(m_1+m_2)}$
2. $\frac{p^2}{2\sqrt{m_1{m}_2}}$
3. $\frac{p^2}{2(m_1-m_2)}$
4. $\frac{p^2(m_1+m_2)}{2m_1{m}_2}$

Q. If a bomb of mass $3mkg$ explodes into two pieces of mass $m$ kg and $2mkg$, the velocity of mass $m$ kg is $16m{s}^{-1}$, then the total kinetic energy released in the explosion will be

1. $96mJ$
2. $116mJ$
3. $192mJ$
4. $384mJ$

Q. Two bodies in space start moving towards each other, due to the gravitational force between them. Which of the following is true for these two bodies, assuming there are no other forces acting on them?

1. The total energy is constant throughout this process
2. Energy is maximum when the distance between them is maximum
3. Internal energy decreases with time
4. The total kinetic energy increases with time