The magnetic intensity at the centre of a long current carrying solenoid is found to be \(1.6 \times 10^3 Am ^{-1}\). If the number of turns is 8 per cm, then the current flowing through the solenoid is \(................\,A\)

A child of mass \(5\,kg\) is going round a merry-goround that makes \(1\) rotation in \(3.14\,s\). The radius of the merry-go-round is \(2\,m\). The centrifugal force on the child will be \(.......\,N\)

Voltage rating of a parallel plate capacitor is \(500\,V\). Its dielectric can withstand a maximum electric field of \({10^6}\,\frac{V}{m}\). The plate area is \(10^{-4}\, m^2\) . What is the dielectric constant if the capacitance is \(15\, pF\) ? (given \({ \in _0} = 8.86 \times {10^{ - 12}}\,{C^2}\,/N{m^2}\))

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.
Reason (R) : For a central force field the angular momentum is a constant.
In the light of the above statements, choose the most appropriate answer from the options given below :

The position of a projectile launched from the origin at \(t = 0\) is given by \(\vec r = \left( {40\hat i + 50\hat j} \right)\,m\) at \(t = 2\,s\). If the projectile was launched at an angle \(\theta\) from the horizontal, then \(\theta\) is (take \(g = 10\, ms^{-2}\))

The electric field of an electromagnetic wave in free space is \(\overrightarrow{\mathrm{E}}=57 \cos \left[7.5 \times 10^6 \mathrm{t}-5 \times 10^{-3}(3 x+4 y)\right](4 \hat{i}-3 \hat{j}) N / C\). The associated magnetic field in Tesla is _______.

A Young's doublc\(-\)slit experiment is performed using monochromatic light of wavelength \(\lambda\). The intensity of light at a point on the screen, where the path difference is \(\lambda,\) is \(K\) units. The intensity of light at a point where the path difference is A \(\frac{\lambda}{6}\) is given by \(\frac{n K}{12},\) where \(n\) is an integer. The value of \(n\) is\(......\)

If \(\overrightarrow{ P } \times \overrightarrow{ Q }=\overrightarrow{ Q } \times \overrightarrow{ P },\) the angle between \(\overrightarrow{ P }\) and \(\overrightarrow{ Q }\) is \(\theta\left(0^{\circ} < \theta < 360^{\circ}\right) .\) The value of \(\theta\) will be ........

A \(2 \,{kg}\) steel rod of length \(0.6\, {m}\) is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so that the rod falls under gravity, Ignoring the friction due to clamping at its lower end, the speed of the free end of rod when it passes through its lowest position is \(\ldots \ldots \ldots \ldots \,{ms}^{-1}\). (Take \(g = 10\, {ms}^{-2}\) )

A physical quantity \(z\) depends on four observables \(a,\) \(b,\) \(c\) and \(d ,\) as \(z =\frac{ a ^{2} b ^{\frac{2}{3}}}{\sqrt{ c } d ^{3}} .\) The percentage of error in the measurement of \(a, b, c\) and \(d\) are \(2 \%, 1.5 \%, 4 \%\) and \(2.5 \%\) respectively. The percentage of error in \(z\) is\(......\%\)

This question has Statement \(-1\) and Statement \(-2\). Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement \(1\) : Very large size telescopes are reflecting telescopes instead of refracting telescopes. Statement \(2\) : It is easier to provide mechanical support to large size mirrors than large size lenses.