A shot is travelling at a rate of \(80\frac{m}{s}\) is just able to pierce a plank of \(4cm\) thick. How much velocity is required such that it just pierce a plank of thickness \(9cm\).
Ans: \(V’=120\frac{m}{s}\).
A running man has half the kinetic energy that of a boy of half his mass. The man speeds up by \(2\frac{m}{s}\) and then has the same kinetic energy as of the boy. What were the original speed of man and the boy?
Ans: \(V_{man}=4.80\frac{m}{s}\) and \(V_{boy}=9.661\frac{m}{s}\).
An electron and a proton are deflected in a cosmic ray experiment. The first with kinetic energy \(10KeV\) and other with \(100KeV\). Which is faster, the electro or the proton? Obtain the ration of their speeds? Given: \(m_{e}=\left(9.11\times10^{-31}\right)kg\) and \(m_{p}=\left(1.67\times10^{-27}\right)kg\), and \(1eV=\left(1.6\times10^{-19}\right)J\).
Ans: \(\frac{v_{e}}{v_{p}}=13.54\). hence; Electron moves faster than proton.
Two bodies A and B having masses \(m_{A}\) and \(m_{B}\) respectively have equal kinetic energy. If, \(p_{A}\) and \(p_{B}\) are their respective momentums then prove that the ration of their momentums is equal \(\sqrt{m_{A}}:\sqrt{m_{B}}\).
Two identical blocks of mass \(10kg\) are moving with same speed \(3\frac{m}{s}\) towards each other along a frictionless horizontal surface. The blocks collides and stick together and comes to rest. What will be the work done by (i) External Force and (ii) Internal force?
Ans:(i) \(W_{ext}=0(Zero)\) and (ii) \(W_{int}=-90J\).
If the momentum of the body is increased by\(20\%\), what will be the increase in the K.E of the body.
Ans: \(44\%\).
K.E of particle is increased by (a) \(100\%\) and (b) \(1\%\). Find: the percentage change in momentum.
Ans: (a) \(41.4\%\) and \(0.5\%\).
The kinetic energy of a body is decreased by \(19\%\). What is the percentage decrease in its linear momentum?
Ans: \(10\%\).
At; \(t=0Sec.\), particle starts moving along the x-axis. Calculate: the net force acting on the particle if the K.E increases uniformly with time.
Ans: \(F\propto \frac{1}{\sqrt{t}}\).
In ballistics demonstration, a police officer fires a bullet of mass \(50.0g\) with speed \(200\frac{m}{s}\) on soft plywood of thickness \(2.00cm\). The bullet emerges with only \(10\%\) of its initial kinetic energy. What will be the emergent speed of the bullet?
Ans: \(63.2\frac{m}{s}\).
A toy rocket of mass \(0.1kg\) has a small amount of fuel of mass \(0.02kg\) which burns out in \(3s\). Starting from the rest on a smooth horizontal track its gets a speed of \(20\frac{m}{s}\) after the fuel is completely burnt out. What is the approximate thrust on the rocket? What is the energy content per gram of the fuel? (Ignore the small variation of mass due to burning of fuel).
Ans:(a) \(F_{Thrust}=\frac{2}{3}N\) and (b) \(\frac{Energy}{gram}=1000\frac{J}{g}\).
A block of mass \(1kg\), moving on a horizontal surface with speed \(v_{i}=2\frac{m}{s}\) enters through a rough surface ranging from \(x=0.1m\) to \(x=2.01m\). The retarding force \(F_{r}\) on the block in this range is inversely proportional to \(x\) over this range. \(F_{r}=\frac{-k}{x}\) for \(0.1m<x<2.01m\). \(F_{r}=0(Zero)\) for \(x<0.1m\) and \(x>2.01m\). Where; \(k=0.5J\). What is the final Kinetic Energy and speed \(v_{f}\) of the block as it crosses the rough patch?
Ans: \(K.E_{f}=0.5J\) and \(v_{f}=1.0\frac{m}{s}\)
A body of mass \(0.5kg\) is taken up an inclined plane of length \(10m\) and height \(5m\) and then allowed to slide down to the bottom again. The co-efficient of friction between the body and the plane is \(0.15\). What is the (a) Work done by the gravitational force over the round trip? (b) Work done by the applied force over the upward journey? (c) Work done by the frictional force in round trip? (d) K.E of the body at the end of the trip?
Ans:(a) \(W_{gra}=0(Zero)\), (b) \(W_{App.Force}=18.5J\), (c) \(W_{fric}=-7.6J\) and (d) \(K.E=10.9J\).
