A force on an object of mass \(100\, g\) is \((10 \hat{i}+5 \hat{j}) N\). The position of that object at \(t=\) \(2 s\) is \((a \hat{i}+b \hat{j}) m\) after starting from rest. The value of \(\frac{a}{b}\) will be..........

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings \(5.50\, mm , 5.55\, mm ,\)\( 5.45\, mm ; 5.65\, mm .\) The average of these four readings is \(5.5375\, mm\) and the standard deviation of the data is \(0.07395\, mm .\) The average diameter of the pencil should therefore be recorded as

Given below are two statements Statement \(I:\) The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination. Statement \(II\) : The resistivity of the material is independent of temperature. In the light of the above statements, choose the correct answer from the options given below

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be..... \(\%\).

The aperture diameter of a telescope is \(5\; \mathrm{m} .\) The separation between the moon and the earth is \(4 \times 10^{5} \;\mathrm{km} .\) With light of wavelength of \(5500\;\mathring A\), the minimum separation between objects on the surface of moon, so that they are just resolved, is close to......\(m\)

The explosive in a Hydrogen bomb is a mixture of \({ }_1 \mathrm{H}^2,{ }_1 \mathrm{H}^3\) and \({ }_3 \mathrm{Li}^6\) in some condensed form. The chain reaction is given by \( { }_3 \mathrm{Li}^6+{ }_0 \mathrm{n}^1 \rightarrow{ }_2 \mathrm{He}^4+{ }_1 \mathrm{H}^3 \) \( { }_1 \mathrm{H}^2+{ }_1 \mathrm{H}^3 \rightarrow{ }_2 \mathrm{He}^4+{ }_0 \mathrm{n}^1\) During the explosion the energy released is approximately [Given : \(\mathrm{M}(\mathrm{Li})=6.01690\  \mathrm{amu} . \mathrm{M}\left({ }_1 \mathrm{H}^2\right)=2.01471 \  amu.\) \(\mathrm{M}\left({ }_2 \mathrm{He}^4\right)=4.00388\  \mathrm{amu}\),\( and\ \)\(1 \ \mathrm{amu}=931.5\) \(\mathrm{MeV}]\)

The bulk modulus of a liquid is \(3 \times 10^{10}\, Nm ^{-2}\). The pressure required to reduce the volume of liquid by \(2 \%\) is  ........ \(\times 10^{8}\; Nm ^{-2}\)

In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is :

Which of the four resistances \(P, Q, R\) and \(S\) generate the greatest amount of heat when a current flows from \(A\) to \(B\) ?

A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is \(\sqrt{\frac{2}{x}}\). The value of \(x\) is \(.......\)