With what angular velocity the earth should spin in order that a body lying at 30° latitude may become weightless [R is radius of earth and g is acceleration due to gravity on the surface of earth]

A man of mass m starts falling towards a planet of mass M and radius R. As he reaches near to the surface, he realizes that he will pass through a small hole in the planet. As he enters the hole, he sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass and a point mass at the center. Change in the force of gravity experienced by the man is

Man outside the shell is 2GMm/3R^2

If the radius of the earth be increased by a factor of 5, by what factor its density be changed to keep the value of g the same?

A spherical hole of radius R/2 is excavated from the asteroid of mass M as shown in fig. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is

A steady flow of water passes along a horizontal tube from a wide section X to the narrower section Y, see figure. Manometers are placed at P and Q at the sections. Which of the statements A, B, C, D, E is most correct?

A cylindrical vessel is filled with a liquid up to height H. A small hole is made in the vessel at a distance y below the liquid surface as shown in figure. The liquid emerging from the hole strike the ground at distance x

A tank is filled upto a height h with a liquid and is placed on a platform of height h from the ground. To get maximum range x_m a small hole is punched at a distance of y from the free surface of the liquid. Then

Figure shows a siphon. Choose the wrong statement

The spring balance A reads 2 kg with a block m suspended from it. A balance B reads 5 kg when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in the figure in this situation

The vessel shown in the figure has two sections. The lower part is a rectangular vessel with area of cross-section A and height h. The upper part is a conical vessel of height h with base area ‘A’ and top area ‘a’ and the walls of the vessel are inclined at an angle 30° with the vertical. A liquid of density r fills both the sections upto a height 2h. Neglecting atmospheric pressure.

A soap bubble has radius R and thickness d (<< R) as shown. It colapses into a spherical drop. The ratio of excess pressure in the drop to the excess pressure inside the bubble is

A liquid is filled in a spherical container of radius R till a height h. At this positions the liquid surface at the edges is also horizontal. The contact angle is

A spherical ball of density r and radius 0.003m is dropped into a tube containing a viscous fluid filled up to the 0 cm mark as shown in the figure. Viscosity of the fluid = 1.260 Nm^–2 and its density L= 2 = 1260 kgm^–3. Assume the ball reaches a terminal speed by the 10 cm mark. The time taken by the ball to traverse the distance between the 10 cm and 20 cm mark is
(g = acceleration due to gravity = 10 ms^–2)

A cubical block of side ‘a’ and density ‘’ slides over a fixed inclined plane with constant velocity ‘v’. There is a thin film of viscous fluid of thickness ‘t’ between the plane and the block. Then the coefficient of viscosity of the thin film will be:

The three water filled tanks shown have the same volume and height. If small identical holes are punched near this bottom, which one will be the first to get empty

Equal volumes of two immiscible liquids of densities r and 2r are filled in a vessel as shown in figure. Two small holes are punched at depth h/ 2 and 3h/2 from the surface of lighter liquid. If v₁ and v₂ are the velocities of a flux at these two holes, then v₁ /v₂ is