Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to \(A\) and \(T,\)  respectively. At time \(t=0\) one particle has displacement \(A\) while the other one has displacement \(\frac {-A}{2}\) and they are moving towards each other. If they cross each other at time \(t,\) then \(t\) is

A butterfly is flying with a velocity \(4 \sqrt{2} \,{m} / {s}\) in North-East direction. Wind is slowly blowing at \(1\) \({m} / {s}\) from North to South. The resultant displacement of the butterfly in \(3\, seconds\) is \(....\,{m}.\)

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

A flask contains hydrogen and oxygen in the ratio of \(2: 1\) by mass at temperature \(27^{\circ} C\). The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :

The de-Broglie wavelength associated with the electron in the \(n\, = 4\) level is

A series \(LR\) circuit connected with an ac source \(E=(25 \sin 1000 t)\  V\) has a power factor of \(\frac{1}{\sqrt{2}}\). If the source of emf is changed to \(E=(20 \sin 2000 t)\ V,\) the new power factor of the circuit will be _______.

The magnetic field vector of an electromagnetic wave is given by \({B}={B}_{o} \frac{\hat{{i}}+\hat{{j}}}{\sqrt{2}} \cos ({kz}-\omega {t})\); where \(\hat{i}, \hat{j}\) represents unit vector along \({x}\) and \({y}\)-axis respectively. At \(t=0\, {s}\), two electric charges \(q_{1}\) of \(4\, \pi\) coulomb and \({q}_{2}\) of \(2 \,\pi\) coulomb located at \(\left(0,0, \frac{\pi}{{k}}\right)\) and \(\left(0,0, \frac{3 \pi}{{k}}\right)\), respectively, have the same velocity of \(0.5 \,{c} \hat{{i}}\), (where \({c}\) is the velocity of light). The ratio of the force acting on charge \({q}_{1}\) to \({q}_{2}\) is :-

The temperature of a metal strip having coefficient of linear expansion \(\alpha\) is increased from \(T_1\) to \(T_2\) resulting in increase of its length by \(\Delta L_1\). The temperature is further increased from \(T_2\) to \(T_3\) such that the increase in its length is \(\Delta L_2\). Given \(T_3+T_1=2T_2\) and \(T_2-T_1=\Delta T\), the value of \(\Delta L_2\) is ______.

An electron moves through a uniform magnetic field \(\vec{B}=B_0 \hat{i}+2 B_0 \hat{j} T\). At a particular instant of time, the velocity of electron is \(\overrightarrow{\mathrm{u}}=3 \hat{i}+5 \hat{j} \mathrm{~m} / \mathrm{s}\). If the magnetic force acting on electron is \(\vec{F}=5 e\hat kN\), where \(e\) is the charge of electron, then the value of \(\mathrm{B}_0\) is _______\(\mathrm{T}\).

A square Lamina OABC of length 10 cm is pivoted at 'O'. Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is :