Mathematics Tes...

A copper sphere of 10 cm diameter is lowered into a water filled hemispherical copper vessel of 20 cm diameter so that the sphere and the vessel becomes concentric. Electrical conductivity of water isσ = 10^-3S/m. The electrical resistance between the sphere and the vessel is:

If a gas is heated at constant pressure then what percentage of total heat supplied is used for doing work ? (Given : for gas = 4/3)

A wet open umbrella is held vertical and it whirld about the handle at a uniform rate of 21 revolutions in 44s. If the rim of the umbrella is circle of 1m in diameter and the height of the rim above the flour is 4.9m, the locus of the drop is a circle of radius.

Fig. shows a uniform solid block of mass M and edge lengths a, b and c . Its M.I about an axis passing through one corner and perpendicular (as shown) to the large face of the block is :

The radius of gyration of a body about an axis at a distance 6 cm from its centre of mass is 10 cm. Then, its radius of gyration about a parallel axis through its centre of mass will be :

A uniform triangular plate ABC of moment of mass m and inertia I (about an axis passing through A and perpendicular to plane of the plate) can rotate freely in the vertical plane about point 'A' as shown in figure. The plate is released from the position shown in the figure. Line AB is horizontal. The acceleration of center of mass just after the release of plate is :

Identify the correct order in which the ratio of radius of gyration to radius increases for the following bodies.

I) rolling solid sphere

II) rolling solid cylinder

III) rolling hollow cylinder

IV) rolling hollow sphere

A uniform meter scale of mass 1kg is placed on table such that a part of the scale is beyond the edge. If a body of mass 0.25kg is hung at the end of the scale then the minimum length of scale that should lie on the table so that it does not tilt is :