The cylindrical tube of a spray pump has a radius \(R,\) one end of which has \(n\) fine holes, each of radius \(r.\) If the speed of the liquid in the tube is \(v,\) the speed of the ejection of the liquid through the holes is:
1. | \(\dfrac{vR^{2}}{n^{2}r^{2}}\) | 2. | \(\dfrac{vR^{2}}{nr^{2}}\) |
3. | \(\dfrac{vR^{2}}{n^{3}r^{2}}\) | 4. | \(\dfrac{v^{2}R}{nr}\) |
Point masses \(m_1\) and \(m_2\), are placed at the opposite ends of a rigid rod of length \(L\) and negligible mass. The rod is set into rotation about an axis perpendicular to it. The position of point \(P\) on this rod through which the axis should pass so that the ork required to set the rod rotating with angular velocity is minimum is given by:
1. | \(x = \frac{m_1L}{m_1+m_2}\) | 2. | \(x= \frac{m_1}{m_2}L\) |
3. | \(x= \frac{m_2}{m_1}L\) | 4. | \(x = \frac{m_2L}{m_1+m_2}\) |
Moving perpendicular to field \(B\), a proton and an alpha particle both enter an area of uniform magnetic field \(B\). If the kinetic energy of the proton is \(1~\text{MeV}\) and the radius of the circular orbits for both particles is equal, the energy of the alpha particle will be:
1. \(4~\text{MeV}\)
2. \(0.5~\text{MeV}\)
3. \(1.5~\text{MeV}\)
4. \(1~\text{MeV}\)
A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches \(30^\circ\), the box starts to slip and slides \(4.0\) m down the plank in \(4.0\) s. The coefficients of static and kinetic friction between the box and the plank will be, respectively:
1. | \(0.6\) and \(0.6\) |
2. | \(0.6\) and \(0.5\) |
3. | \(0.5\) and \(0.6\) |
4. | \(0.4\) and \(0.3\) |
An ideal gas is compressed to half its initial volume using several processes. Which of the processes results in the maximum work done on the gas?
1. adiabatic
2. isobaric
3. isochoric
4. isothermal
A ball is thrown vertically downward from a height of \(20\) m with an initial velocity \(v_0\). It collides with the ground, loses \(50\%\) of its energy in a collision, and rebounds to the same height. The initial velocity \(v_0\) is:
(Take, \(g=10~\mathrm{ms^{-2}}\))
1. \(14\) ms–1
2. \(20\) ms–1
3. \(28\) ms–1
4. \(10\) ms–1
In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is:
1. | \(\frac{4}{9}\) | 2. | \(\frac{9}{4}\) |
3. | \(\frac{27}{5}\) | 4. | \(\frac{5}{27}\) |
A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 ms-1 at an angle of with the source-observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air 330 ms-1), is:
1. 100 Hz
2. 103 Hz
3. 106 Hz
4. 97 Hz
If dimensions of critical velocity \({v_c}\) of a liquid flowing through a tube are expressed as \(\eta^{x}\rho^yr^{z}\), where \(\eta, \rho~\text{and}~r\) are the coefficient of viscosity of the liquid, the density of the liquid, and the radius of the tube respectively, then the values of \({x},\) \({y},\) and \({z},\) respectively, will be:
1. \(1,-1,-1\)
2. \(-1,-1,1\)
3. \(-1,-1,-1\)
4. \(1,1,1\)
\(4.0~\text{gm}\) of gas occupies \(22.4~\text{litres}\) at NTP. The specific heat capacity of the gas at a constant volume is \(5.0~\text{JK}^{-1}\text{mol}^{-1}.\) If the speed of sound in the gas at NTP is \(952~\text{ms}^{-1},\) then the molar heat capacity at constant pressure will be:
(\(R=8.31~\text{JK}^{-1}\text{mol}^{-1}\))
1. | \(8.0~\text{JK}^{-1}\text{mol}^{-1}\) | 2. | \(7.5~\text{JK}^{-1}\text{mol}^{-1}\) |
3. | \(7.0~\text{JK}^{-1}\text{mol}^{-1}\) | 4. | \(8.5~\text{JK}^{-1}\text{mol}^{-1}\) |