Two tubes of radii r₁ and r₂, and lengths l₁ and l₂ , respectively, are connected in series and a liquid flows through each of them in stream line conditions. P₁ and P₂ are pressure differences across the two tubes.

If P₂ is 4P₁ and l₂ is $${{{1_1}} \over 4}$$, then the radius r₂ will be equal to :

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of:

A thin 1 m long rod has a radius of 5 mm. A force of 50 $$\pi $$kN is applied at one end to determine its Young’s modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false ?

A bottle has an opening of radius a and length b. A cork of length b and radius (a + $$\Delta $$a) where ($$\Delta $$a < < a) is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is $$\mu $$ then the force needed to push the cork into the bottle is :