A clock has a continuously moving second's hand of \(0.1\, m\) length. The average acceleration of the tip of the hand (in units of \(ms ^{-2}\) ) is of the order of

In a photoelectric effect experiment a light of frequency \(1.5\) times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electrons emitted will be _______.

In a simple pendulum experiment for determination of acceleration due to gravity \((g)\), time taken for \(20\) oscillations is measured by using a watch of \(1\, second\) least count. The mean value of time taken comes out to be \(30\,s\). The length of pendulum is measured by using a meter scale of least count \(1\, mm\) and the value obtained is \(55.0\, cm\). The percentage error in the determination of \(g\) is close to  ........... \(\%\)

Two beams, \(A\) and \(B\), of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam \(A\) has maximum intensity ( and beam \(B\) has zero intensity), a rotation of polaroid through \(30 ^o \) makes the two beams appear equally bright. If the initial intensities of the two beams are \(I_A\) and \(I_B\)  respectively, then \(\frac{{{I_A}}}{{{I_B}}}\)=

The centre of mass of a solid hemisphere of radius \(8\, cm\) is \(X \,cm\) from the centre of the flat surface. Then value of \(x\) is\(......\)

An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave.

The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N , the length of the string is 1.56 m. The original length of the string is _____ m.

The time taken by a block of mass \(m\) to slide down from the highest point to the lowest point on a rough inclined plane is \(50\%\) more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at \(45^\circ\) with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is _____.

Given below are two statements: Statement \(I\): An \(AC\) circuit undergoes electrical resonance if it contains either a capacitor or an inductor. Statement \(II\): An \(AC\) circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor. In the light of above statements, choose the correct answer from the options given below

A string is clamed at both the ends and it is vibrating in its \(4^{th}\) harmonic. The equation of the stationary wave is \(Y =0.3\,sin\,(0.157\,x) \,cos\,(200\pi t)\). The length of the string is ..... \(m\) (all quantities are in \(SI\) units)