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 \(........... W\)

The velocity of water in a river is \(18\, km/h\) near the surface. If the river is \(5\, m\) deep, find the shearing stress between the horizontal layers of water. The co-efficient of viscosity of water \(= 10^{-2}\,,poise\)

Pressure inside a soap bubble is greater than the pressure outside by an amount _______. (given : \(\mathrm{R}=\) Radius of bubble, \(\mathrm{S}=\) Surface tension of bubble)

A thin bar of length \(L\) has a mass per unit length \(\lambda \), that increases linearly with distance from one end. If its total mass is \(M\) and its mass per unit length at the lighter end is \(\lambda_0\), then the distance of the centre of mass from the lighter end is

In an experiment the values of two spring constants were measured as \(k _1=(10 \pm 0.2) N / m\)
and \(k _2=(20 \pm 0.3) N / m\). If these springs are connected in parallel, then the percentage error in equivalent spring constant is :

In order to determine the Young's Modulus of a wire of radius \(0.2\, cm\) (measured using a scale of least count \(=0.001\, cm )\) and length \(1 \,m\) (measured using a scale of least count \(=1\, mm\) ), a weight of mass \(1\, kg\) (measured using a scale of least count \(=1 \,g\) ) was hanged to get the elongation of \(0.5\, cm\) (measured using a scale of least count \(0.001\, cm\) ). What will be the fractional error in the value of Young's Modulus determined by this experiment? (in \(\%\))

A fish rising vertically upward with a uniform velocity of \(8\,ms ^{-1}\), observes that a bird is diving vertically downward towards the fish with the velocity of \(12\,ms ^{-1}\). If the refractive index of water is \(\frac{4}{3}\), then the actual velocity of the diving bird to pick the fish, will be \(.......\,ms ^{-1}\).

The velocity of sound in air is doubled when the temperature is raised from \(0^{\circ} C\) to \(\alpha^{\circ} C\). The value of \(\alpha\) is ________.

The surface tension of a soap solution is \(3.5 \times 10^{-2}\) N/m. The work required to increase the radius of a soap bubble from \(1\) cm to \(2\) cm is \(\alpha \times 10^{-6}\) J. The value of \(\alpha\) is _____. (\(\pi = 22/7\))