A bowl with a semi spherical base is designed such that its centre of gravity is located at the centre of curvature of the spherical part. Explain giving reasons, to which state of equilibrium the bowl belongs. If the bowl is filled with water upto the centre of gravity, explain how the equilibrium state would be affccted/unaffccted.

Explain how the position of the centre of gravity determines whether a body is in stable or unstable equilibrium.

A cricket bat is cut through its centre of mass into two parts as shown. Then, state whether both parts are of same mass or not, Also explain reason.

A fish is near the centre of a spherical water filled( mu=4//3 )fish bowl,A child stands in air ata distance 2R (R is the radius of curvature of the sphere)from the centre of the bowl.At what distance from the centre would the child nose appear to the fish situated at the centrer:

Assertion : For a floating body to be in stable equilibrium, its centre of buoyancy must be located above the centre of gravity. Reason : The torque produced by the weight of the body and the upthrust will restore body back to its normal position, after the body is disturbed.

(i) A non uniform cube of side length a is kept inside a container as shown in the figure. The average density of the material of the cube is 2 rho where rho is the density of water. Water is gradually fille din the container. It is observed that the cube begins to topple, about its edge into the plane of the figure passing through pointA, when the height of the water in the container becomes (a)/(2) . Find the distance of the centre of mass of the cube from the face AB of the cube. Assume that water seeps under the cube. (ii) A rectangular concrete block (specific gravity =2.5) is used as a retatining wall in a reservoir of water. The height and width of the block are x and y respectively the height of water in the reservoir is z=(3)/(4)x . the concrete block cannot slide on the horizontal base but can rotate about an axis perpendicular to the plane of the figure and passing through point A (a) Calculate the minimum value of the ratio (y)/(x) for which the block will not begin to overturn about A. (b) Redo the above problem for the case when there is a seepage and a thin film of water is present under the block. Assume that a seal at A prevents the water from flowing out underneath the block.

A spherical shaped fish bowl filled with water of refractive index 1.3 is placed in another large tank filled with another liquid of refractive index 1.4 such that rim of the fish bowl is slightly above the liquid filled in the tank. The diameter of the fish bowl is 20 cm. A parallel light rays from a distant object is incident on the spherical fish bowl. Find the position at which incident light rays will get focused when seen by a small fish at the centre of the bowl.

We know that parallel light rays which are inclined to the principal axis of a spherical mirror, after reflection converge at a point in the focal plane of the mirror. With this knowledge explain how you will trace the reflected ray for incident ray PQ shown in the Fig. F is focus and C is centre of curvature of the mirror.

A beaker of radius r is filled with water (refractive index (4)/(3) ) up to a height H as shown in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed omega . This makes the water surface curved so that the difference in the height of water level at the centre and the circumference of the beaker is h (h lt lt H, h lt lt r) as shown in the figure on the right . Take this surface to be approximately spherical with a radius of curvalture R . Which of the following is/are correct ? (g is acceleration due to gravity)