Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of \(3\,s\) and \(4\,s\) respectively. If their moments of inertia are in the ratio of \(3: 2\) then the ratio of their magnetic moments will e.

The area of cross-section of a large tank is \(0.5 \; m ^{2}\). It has a narrow opening near the bottom having area of cross-section \(1 \; cm ^{2}\). A load of \(25 \; kg\) is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is \(40 \; cm\) above the bottom, will be \(\dots \; cms ^{-1}\). \(\left[\right.\) Take \(\left.g =10 \; ms ^{-2}\right]\)

In an experiment with a closed organ pipe, it is filled with water by \(\left(\frac{1}{5}\right)\) th of its volume. The frequency of the fundamental note will change by

Consider an equilateral prism (refractive index \( \sqrt{2} \)). A ray of light is incident on its one surface at a certain angle i. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to __________ .

A \(2\,meter\) long scale with least count of \(0.2\,cm\) is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at \(80\,cm\) mark and \(1\,m\) mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at \(180\,cm\) mark. The \(\%\) error in the estimation of focal length is

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 :

This question has Statement-I and Statement-2. Of the four ch.oices given after the Statements, choose the one that best describes the two Statetnents. Statement \(-1\) : A capillary is dipped in a liquid and liquid rises to a height \(h\) in it. As the temperature of the liquid is raised, the height \(h\) increases (if the density of the liquid and the angle of contact remain the same). Statement \(-2\) : Surface tension of a liquid decreases with the rise in its temperature.

If \(\overrightarrow{\mathrm{L}}\) and \(\overrightarrow{\mathrm{P}}\) represent the angular momentum and linear momentum respectively of a particle of mass ' m ' having position vector \(\overrightarrow{\mathrm{r}}=\mathrm{a}(\hat{\mathrm{i}} \cos \omega \mathrm{t}+\hat{\mathrm{j}} \sin \omega \mathrm{t})\). The direction of force is

An object is placed at a distance of \(12 \,{cm}\) from a convex lens. A convex mirror of focal length \(15 \,{cm}\) is placed on other side of lens at \(8 \,{cm}\) as shown in the figure. Image of object coincides with the object.When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be ..... \((cm)\)

A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively \(\left( k _{\text {sph }}: k _{ cyl }\right)\) is \(2: \sqrt{ x }\), then value of \(x\) is .............