When the position vector \(\overrightarrow{ r }=x \hat{ i }+y \hat{ j }+z \hat{ k }\) changes sign as \(-\overrightarrow{ r }\), which one of the following vector will not flip under sign change ?

A particle of mass \( m\) moving in the \(x\) direction with speed \(2v\) is hit by another particle of mass \(2m\) moving in the \(y\) direction with speed \(v\). If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to .............. \(\%\)

Given below are two statements : \(Statement\) \(I\) : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model. \(Statement\) \(II\) : An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model. In the light of the above statements, choose the most appropriate from the options given below.

A two point charges \(4 q\) and \(-q\) are fixed on the \(x-\)axis at \(x=-\frac{d}{2}\) and \(x=\frac{d}{2},\) respectively. If a third point charge \('q'\) is taken from the origin to \(x = d\) along the semicircle as shown in the figure, the energy of the charge will

An electron with kinetic energy \(K _{1}\) enters between parallel plates of a capacitor at an angle \('\alpha'\) with the plates. It leaves the plates at angle \(' \beta '\) with kinetic energy \(K _{2}\). Then the ratio of kinetic energies \(K _{1}: K _{2}\) will be ....... .

In the given circuit the \({AC}\) source has \(\omega=100\, {rad} {s}^{-1}\). Considering the inductor and capacitor to be ideal, what will be the current \(I\) flowing through the circuit? (in \(A\))

The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is \(\left(\frac{x}{100}\right) \% .\) If the relative errors in measuring the mass and the diameter are \(6.0 \%\) and \(1.5 \%\) respectively, the value of \(x\) is

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by \(E _{ x }= E _0 \sin ( kz -\omega t )\) \(B _{ y }= B _0 \sin ( kz -\omega t )\) Then the correct relation between \(E_0\) and \(B_0\) is given by

Three rods of Copper, Brass and Steel are welded together to form a \(Y\) shaped structure. Area of cross - section of each rod \(= 4\ cm^2\) . End of copper rod is maintained at \(100^o C \) where as ends ofbrass and steel are kept at \(0^o C\). Lengths of the copper, brass and steel rods are \(46, 13\) and \(12\ cms\) respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are \(0.92, 0.26\) and \(0.12\ CGS\) units respectively. Rate ofheat flow through copper rod is ....... \(cal\, s^{-1}\)

A body of mass \(5\,kg\) is moving with a momentum of \(10\,kg\,ms ^{-1}\). Now a force of \(2\,N\) acts on the body in the direction of its motion for \(5\,s\). The increase in the Kinetic energy of the body is \(...........J\).

A simple pendulum of string length 30 cm performs 20 oscillations in 10s. The length of the string required for the pendulum to perform 40 oscillations in the same time duration is ___________ cm. [Assume that the mass of the pendulum remains same.]

At \(t=0\), a body of mass \(100\) g starts moving under the influence of a force \((5\hat{i}+10\hat{j})\) N. After \(2\) s its position is \((2x\hat{i}+5y\hat{j})\) m. The ratio \(x:y\) is ______.