A copper block of mass \(5.0\, kg\) is heated to a temperature of \(500^{\circ} C\) and is placed on a large ice block. What is the maximum amount of ice (ઇન \(kg\)) that can melt? [Specific heat of copper: \(0.39\, Jg ^{-1 \circ} C ^{-1}\) and latent heat of fusion of water : \(335 \,J g ^{-1}\) ]

The arm \(P Q\) of a rectangular conductor is moving from \(x=0\) to \(x=2 b\) outwards and then inwards from \(x=2 b\) to \(x=0\) as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from \(x=0\) to \(x=b\). Identify the graph showing the variation of different quantities with distance.

A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is \({\theta _{iC}}\) and Brewster's angle of incidence is \({\theta _{iB}}\), such that \(\sin \,{\theta _{iC}}/\sin \,{\theta _{iB}} = \eta  = 1.28\). The  relative refractive index of the two media is

The equivalent resistance of the given circuit between the terminals \({A}\) and \({B}\) is  \(....\Omega\)

A wire of resistance \(R\) is bent to form a square \(ABCD\) as shown in the figure. The effective resistance between \(E\) and \(C\) is ( \(E\) is mid-point of arm \(CD\) )

A thin rod having a length of \(1\; m\) and area of cross-section \(3 \times 10^{-6}\,m ^2\) is suspended vertically from one end. The rod is cooled from \(210^{\circ}\,C\) to \(160^{\circ}\,C\). After cooling, a mass \(M\) is attached at the lower end of the rod such that the length of rod again becomes \(1\,m\). Young's modulus and coefficient of linear expansion of the rod are \(2 \times 10^{11} Nm ^{-2}\) and \(2 \times 10^{-5} K ^{-1}\), respectively. The value of \(M\) is \(.......kg .\left(\right.\) Take \(\left.g=10\,m s ^{-2}\right)\)

The velocity of a particle is \(v = v _{0}+ gt + Ft ^{2}\). Its position is \(x=0\) at \(t=0\); then its displacement after time \(( t =1)\) is :

An alternating voltage \(\mathrm{V}(\mathrm{t})=220 \sin 100 \ \pi \mathrm{t}\) volt is applied to a purely resistive load of \(50\ \Omega\). The time taken for the current to rise from half of the peak value to the peak value is _______.

A particle of mass \(m\) is moving along a trajectory given by
\(x = x_0 + a\, cos\,\omega_1 t\)
\(y = y_0 + b\, sin\,\omega_2t\)
The torque, acing on the particle about the origin, at \(t = 0\) is

A batsman hits back a ball of mass \(0.4 \; kg\) straight in the direction of the bowler without changing its initial speed of \(15 \; ms ^{-1}\). The impulse imparted to the ball is \(\dots \; Ns\)

An observer looks at a distant tree of height \(10\ m\) with a telescope of magnifying power of \(20\). To the observer the tree appears :