\(T\) is the time period of simple pendulum on the earth's surface. Its time period becomes \(x T\) when taken to a height \(R\) (equal to earth's radius) above the earth's surface. Then, the value of \(x\) will be:

For \(z=a^{2} x^{3} y^{\frac{1}{2}}\), where \(a\) is a constant. If percentage error in measurement of \(x\) and \(y\) are \(4 \%\) and \(12 \%\), respectively, then the percentage error for \(z\) will be \(%\)

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth is closest to : [Boltzmans Constant \(k_B = 1.38\times10^{-23}\, J / K\) Avogadro number \(N_A = 6.02\times10^{26}\, / kg\) Radius of Earth \(: 6.4\times10^6\, m\) Gravitation acceleration on Earth \(= 10\, ms^{-2}\)]

An electrical bulb rated \(220\,V , 100\,W\), is connected in series with another bulb rated \(220\,V\), \(60\,W\).If the voltage across combination is \(220\,V\), the power consumed by the \(100\,W\) bulb will be about \(........... W\)

A hemispherical glass body of radius \(10\, cm\) and refractive index \(1.5\) is silvered on its curved surface. A small air bubble is \(6\, cm\) below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen 

The maximum percentage error in the measurment of density of a wire is [Given, mass of wire \(=(0.60 \pm 0.003) \mathrm{g}\)
radius of wire \(=(0.50 \pm 0.01) \mathrm{cm}\)
length of wire \(=(10.00 \pm 0.05) \mathrm{cm}]\)

The fractional compression \(\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)\) of water at the depth of 2.5 km below the sea level is ______ \(\%\). Given, the Bulk modulus of water \(=2 \times 10^9 \mathrm{~N} \mathrm{~m}^{-2}\), density of water \(=10^3\) \(\mathrm{kg} \mathrm{m}^{-3}\), acceleration due to gravity \(=\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\).

Primary side of a transformer is connected to \(230 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. Turns ratio of primary to secondary winding is \(10: 1\). Load resistance connected to secondary side is \(46\  \Omega\). The power consumed in it is :

A moving proton and electron have the same deBroglie wavelength. If \({K}\) and \({P}\) denote the \({KE}\). and momentum respectively. Then choose the correct option :