Your friend is having eye sight problem. She is not able lo see clearly a distant uniform window mesh and it appears to her as non-uniform and distorted. The doctor diagnosed the problem as

For a body executing \(S.H.M. :\) \((a)\) Potential energy is always equal to its \(K.E.\) \((b)\) Average potential and kinetic energy over any given time interval are always equal. \((c)\) Sum of the kinetic and potential energy at any point of time is constant. \((d)\) Average \(K.E.\) in one time period is equal to average potential energy in one time period. Choose the most appropriate option from the options given below:

A car moving with a speed of \(54\) km/h takes a turn of radius \(20\) m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take \(g=10\) m/s\(^2\))

A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity \(0.8\)). The height of water is \(3\,m\) and that of kerosene \(2\,m\). When the hole is opened the velocity of fluid coming out from it is nearly ........ \(ms^{-1}\) .(take \(g\, = 10\, m s^{-2}\) and density of water \(= 10^3\, kg\, m^{-3}\))

The time dependence of the position of a particle of mass \(m = 2\) is given by \(\vec r\,(t)\, = \,2t\,\hat i\, - 3{t^2}\hat j\) Its angular momentum with respect to the origin at time \(t = 2\) is

A particle of mass \(m\) is moving along the side of a square of side '\(a\)', with a uniform speed \(v\) in the \(x-y\) plane as shown in the figure Which of the following statement is false for the angular momentum \(\vec L\) about the origin ?

A Helmholtz coil has pair of loops, each with \(N\) turns and radius \(R\). They are placed coaxially at distance \(R\) and the same current \(I\) flows through the loops in the same direction. The magnitude of magnetic field at \(P\), midway between the centres \(A\) and \(C\), is given by (Refer to figure)

A particle is subjected two simple harmonic motions as :
\(\mathrm{x}_1=\sqrt{7} \sin 5 \mathrm{tcm}\)
and \(x_2=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}\right) \mathrm{cm}\)
where x is displacement and \(t\) is time in seconds. The maximum acceleration of the particle is \(\mathrm{x} \times 10^{-2} \mathrm{~ms}^{-2}\). The value of x is :

The metallic bob of simple pendulum has the relative density \(5\). The time period of this pendulum is \(10\,s\). If the metallic bob is immersed in water, then the new time period becomes \(5 \sqrt{ x } s\). The value of \(x\) will be.

The temperature \(\theta\) at the junction of two insulating sheets, having thermal resistances \(R _{1}\) and \(R _{2}\) as well as top and bottom temperatures \(\theta_{1}\) and \(\theta_{2}\) (as shown in figure) is given by

There is an air bubble of radius \(1.0\,mm\) in a liquid of surface tension \(0.075\,Nm ^{-1}\) and density \(1000\,kg\) \(m ^{-3}\) at a depth of \(10\,cm\) below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is \(....Pa \left( g =10\,ms ^{-2}\right)\)