In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its \(4^{\text {th }}\) division coincides exactly with a certain division on main scale. If \(50\) vernier scale divisions equal to \(49\) main scale divisions and zero error in the instrument is \(0.04 \mathrm{~mm}\) then how many main scale divisions are there in \(1 \mathrm{~cm}\) ?

A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If \(r_{d}\) and \(r_{p}\) are the radii of their circular paths respectively, then the ratio \(\frac{r_{d}}{r_{p}}\) will be \(\sqrt{ x }: 1\) where \(x\) is ..........

The alternating current is given by \({i}=\left\{\sqrt{42} \sin \left(\frac{2 \pi}{{T}} {t}\right)+10\right\} {A}\) The \(r.m.s.\) value of this current is \({A}\)

Given below are two statements :- Statement \(I\) : Davisson-Germer experiment establishes the wave nature of electrons. Statement \(II\) : If electrons have wave nature, they can interfere and show diffraction. In the light of the above statements choose the correct answer from the options given below

A bullet of mass \(200\,g\) having initial kinetic energy \(90\,J\) is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to \(40\,J\) within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is \(.....m\)

Given below are two statements: one is labelled as Assertion \(\mathrm{A}\) and the other is labelled as Reason \(\mathrm{R}\) Assertion A : The kinetic energy needed to project a body of mass m from earth surface to infinity is \(\frac{1}{2} \mathrm{mgR}\), where R is the radius of earth.
Reason \(\mathrm{R}\) : The maximum potential energy of a body is zero when it is projected to infinity from earth surface.
In the light of the above statements, choose the correct answer from the option given below

A cubic block of mass \(m\) is sliding down on an inclined plane at \(60^{\circ}\) with an acceleration of \(\frac{\mathrm{g}}{2}\), the value of coefficient of kinetic friction is

A block of mass \(m\), lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant \(k\). The other end of the spring is fixed, as shown in the figure. The block is initially at rest in a equilibrium position. If now the block is pulled with a constant force \(F\), the maximum speed of the block is

\(0.056 \,kg\) of Nitrogen is enclosed in a vessel at a temperature of \(127\,^{\circ} C\). The amount of heat required to double the speed of its molecules is k cal. (Take \(R =2\) \(cal \,mole\) \(^{-1} K ^{-1}\) )

\(512\) identical drops of mercury are charged to a potential of \(2\, V\) each. The drops are joined to form a single drop. The potential of this drop is ......... \(V.\)

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is \(50 \,\%\) of its translational kinetic energy. The body is :

The current \(I_{1}\) (in \(A\)) flowing through \(1\; \Omega\) resistor in the following circuit is:

An ideal gas has molecules with \(5\,\) degrees of freedom. The ratio of specific heats at constant pressure \((C_p)\) and at constant volume \((C_v)\) is