$A$ thin rectangular magnet suspended freely has a period of oscillation equal to $T.$ Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is $T',$ the ratio $T'/T$ is :-

$A$ black body of mass $34.38 \ g$ and surface area $19.2 \ cm^2$ is at an initial temperature of $400 \ K$. It is allowed to cool inside an evacuated enclosure kept at a constant temperature of $300 \ K$. The rate of cooling is $0.04 \ ^{\circ}C/s$. The specific heat of the body in $J \ kg^{-1} \ K^{-1}$ is (Stefan's constant $\sigma = 5.73 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$)

If the altitudes of a triangle are in arithmetic progression,then the sides of the triangle are in

The magnifying power of a telescope is $9$. When it is adjusted for parallel rays,the distance between the objective and eyepiece is $20 \ cm$. The focal lengths of the lenses are:

$I$ carried $1000\,kg$ of watermelon in summer by train. In the beginning,the water content was $99\%$. By the time $I$ reached the destination,the water content had dropped to $98\%$. The reduction in the weight of the watermelon was $.......\,kg$.

When a glass prism of refracting angle $60^{\circ}$ is immersed in a liquid,its angle of minimum deviation is $30^{\circ}$. The critical angle of glass with respect to the liquid medium is (in $^{\circ}$)