A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is

A small particle of mass m is projected at an angle θ with the x–axis with an initial velocity v₀ in the x–y plane as shown in the figure. At a time t<v_osin/g, the angular momentum of the particle is

The moment of inertia of a uniform cylinder of length

• 1

• 

• 

• 

A slender uniform rod of mass M and length

A thin uniform rod of length

Let P(r) = Qr/πR⁴ be the charge density distribution for a solid sphere of radius R and total charge Q. for a point ‘p’ inside the sphere at distance r₁ from the centre of the sphere, the magnitude of electric field is

• 

• 0

• 
• 

A thin rod of length ‘L’ is lying along the x-axis with its ends at x = 0 and x = L. Its linear density (mass/length) varies with x as, where n can be zero or any positive number. If the position x_CM of the centre of mass of the rod is plotted against ‘n’, which of the following graphs best approximates the dependence of x_CM on n? 

Consider a uniform square plate of side ‘a’ and mass ‘m’. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

• (5/6)ma²

• (1/12)ma²

• (7/12)ma²

• (7/12)ma²

A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α/R from the centre of the bigger disc.The value of α is

• 1/3

• 1/2

• 1/6

• 1/6

A round uniform body of radius R, mass M and moment of inertia ‘I’, rolls down (without slipping) an inclined plane making an angle θ with the horizontal. Then its acceleration is