A thin magnetic iron rod of length \(30 \mathrm{~cm}\) is suspended in a uniform magnetic field. Its time period of oscillation is \(4 \mathrm{~s}\). It is broken into three equal parts. The time period in seconds of oscillation of one part when suspended in the same magnetic field is

A body thrown vertically upwards from the ground reaches a maximum height ' \(h\) '. The ratio of the kinetic and potential energies of the body at a height \(40 \%\) of \(h\) from the ground is

A horizontal aluminium rod of diameter \(4 \mathrm{~cm}\) projected \(6 \mathrm{~cm}\) from a wall. An object of mass \(400 \pi \mathrm{kg}\) is suspended from the end of the rod. The shearing modulus of aluminium is \(3.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^2\). The vertical deflection of the end of the rod is \(\left(\because g=10 \mathrm{~m} / \mathrm{s}^2\right)\)

The need for modulation is

A stone is dropped from a height of \(100 \mathrm{~m}\), while another one is projected vertically upwards from the ground with a velocity of \(25 \mathrm{~m} / \mathrm{s}\) at the same time. The time in seconds after which they will have the same height is (acceleration due to gravity, \(g=10 \mathrm{~ms}^{-2}\) )

From a height of ' \(h\) ' above the ground, a ball is projected up at an angle \(30^{\circ}\) with the horizontal. If the ball strikes the ground with a speed of 1.25 times its initial speed of \(40 \mathrm{~ms}^{-1}\), the value of ' \(h\) ' is (acceleration due to gravity \(=\) \(10 \mathrm{~ms}^{-2}\) )

A small angled prism is made of a material of refractive index \(\frac{3}{2}\). The ratio of the angles of minimum deviations when the prism is placed in air and in water of refractive index \(\frac{4}{3}\) is

An alloy is composed of two radioactive materials \(A\) and \(B\) having equal weight. The half life of \(A\) and \(B\) are 10 yrs and \(20 \mathrm{yrs}\) respectively. After time \(t\), the alloy was found to consist of \(\left(\frac{1}{e}\right) \mathrm{kg}\) of \(A\) and \(1 \mathrm{~kg}\) of \(B\). . If the atomic weight of \(A\) and \(B\) are same, then the value of \(t\) is (Assume, \(\ln 2=0.7\) )

A point object \(O\) is placed on the axis of a cylindrical piece of glass of refractive index 1.6 as shown in the figure. One surface of the glass piece is convex with radius of curvature \(3 \mathrm{~mm}\). The point appeared to be at \(5 \mathrm{~mm}\) on the axis when viewed along the axis and from right side of convex surface. The distance of the point object from the convex surface is :

The ratio of the work done, change in internal energy and heat absorbed when a diatomic gas expands at constant pressure is

Statement (I) : The slope of kinetic energy-displacement curve of a body in motion will be directly proportional to its acceleration. Statement (II) : From a height of \(15 \mathrm{~m}\) a ball is projected vertically upwards with a velocity of \(30 \mathrm{~m} / \mathrm{s}\). If the ball rises to the same height after hitting the ground, the loss of its energy on hitting the ground is \(30 \%\). Statement (III) : The velocity acquired by a body of mass ' \(m\) ' after travelling a fixed distance from rest under the action of a constant force is directly proportional to mass ' \(\mathrm{m}\) '. Which of the following is correct?

A metal chain of mass \(2 \mathrm{~kg}\) and length \(90 \mathrm{~cm}\) over hangs a table with \(60 \mathrm{~cm}\) on the table. How much work needs to be done to put the hanging part of the chain back on the table? \(\left(\right.\) Let \(\left.g=10 \mathrm{~m} / \mathrm{s}^2\right)\)

What is output of the logic circuit shown below?