A body of mass \(0.5\, kg\) travels on straight line path with velocity \(v =\left(3 x ^{2}+4\right) m / s\). The net workdone by the force during its displacement from \(x =0\) to \(x =2\, m\) is\(.......J\)

A car is moving on a horizontal curved road with radius \(50\,m\). The approximate maximum speed of car will be \(............\,ms^{-1}\), if friction between tyres and road is \(0.34.\left[\right.\) Take \(\left.g =10 ms ^{-2}\right]\)

A parallel plate capacitor having a separation between the plates \(d\) , plate area \(A\) and material with dielectric constant \(K\) has capacitance \(C_0\). Now one-third of the material is replaced by another material with dielectric constant \(2K\), so that effectively there are two capacitors one with area \(\frac{1}{3}\,A\) , dielectric constant \(2K\) and another with area \(\frac{2}{3}\,A\) and dielectric constant \(K\). If the capacitance of this new capacitor is \(C\) then \(\frac{C}{{{C_0}}}\) is

An inductor of \(0.5\,mH\), a capacitor of \(20\,\mu\,F\) and resistance of \(20\,\Omega\) are connected in series with a \(220\,V\) ac source. If the current is in phase with the emf, the amplitude of current of the circuit is \(\sqrt{x} A\). The value of \(x\) is -

A raindrop with radius \(R=0.2\, {mm}\) fells from a cloud at a height \(h=2000\, {m}\) above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attainde by the raindrop is : (In \({ms}^{-1}\)) [Density of water \(f_{{w}}=1000\;{kg} {m}^{-3}\) and density of air \(f_{{a}}=1.2\; {kg} {m}^{-3}, {g}=10 \;{m} / {s}^{2}\) Coefficient of viscosity of air \(=18 \times 10^{-5} \;{Nsm}^{-2}\) ]

A monoatomic gas having \(\gamma=\frac{5}{3}\) is stored in a thermally insulated container and the gas is suddenly compressed to \(\left(\frac{1}{8}\right)^{\text {th }}\) of its initial volume. The ratio of final pressure and initial pressure is: ( \(\gamma\) is the ratio of specific heats of the gas at constant pressure and at constant volume)

The total charge on the system of capacitance \(C _{1}=1\,\mu F , C _{2}=2\,\mu F , C _{3}=4\,\mu F\) and \(C _{4}=3\,\mu F\) connected in parallel is \(......\mu C\) (Assume a battery of \(20\,V\) is connected to the combination)

When a particle executes \(SHM\) the nature of graphical representation of velocity as a function of displacement is :

When two soap bubbles of radii \(a\) and \(b ( b > a )\) coalesce, the radius of curvature of common surface is

A capacitor P with capacitance \( 10\times10^{-6} F \) is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor P is connected across another capacitor Q with capacitance \( 20\times10^{-6} F \). The charge on capacitor Q when equilibrium is established will be \( \alpha\times10^{-5} C \).(assume capacitor \(Q\) does not have any charge initially),The value of \( \alpha \) is __________ .

The resistance of a galvanometer is \(50\, ohm\) and the maximum current which can be passed through it is \(0.002\, A\). What resistance must be connected to it in order to convert it into an ammeter of range \(0 -0.5\, A\) ?....\(ohm\)

Two strings (A, B) having linear densities \(\mu_{ A }=2 \times 10^{-4} kg / m\) and \(\mu_{ B }=4 \times 10^{-4} kg / m\) and lengths \(L _{ A }=2.5 m\) and \(L _{ B }=1.5 m\) respectively are joined. Free ends of A and B are tied to two rigid supports C and D , respectively creating a tension of 500 N in the wire. Two identical pulses, sent from \(C\) and \(D\) ends, take time \(t_1\) and \(t_2\), respectively, to reach the joint. The ratio \(t_1 / t_2\) is :

The time period of a satellite revolving around earth in a given orbit is \(7 \,hours\). If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be ...... \(hours\)