Hooke’s Law - Practice Questions & MCQ

A wire elongates by $l\mathrm{mm}$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends, the elongation of the wire will be (in mm )

A bottle has an opening of radius a and length b.  A cork of length b and radius (a + a) where (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 µ then the force needed to push the cork into  the bottle is :

A thin steel ring of inner radius r and cross-section area A to be mounted on a wheel of radius $R(R>r)$. If the Young modulus of the metal ring is Y then the tension in the steel ring is

A rod, of length $L$ at room temperature and uniform area of cross-section $A$, is made of a metal having a coefficient of linear expansion $\alpha /{}^{\circ }\mathrm{C}$. It is observed that an external compressive force F, is applied on each of its ends, and prevents any change in the length of the rod when its temperature rises by $\mathrm{\Delta }TK$. Young's modulus, Y, for this metal, is:

The maximum stretching force of humans is $81\times {10}^4\mathrm{V}$, However the Young's modulus for stretch is $36\times {10}^9\mathrm{Pa}$. Then what is longitudinal strain $(\frac{{\mathrm{\Delta }}_l}{l}=?)⟶(A=9{\mathrm{cm}}^2)$

According to Hooke's law of elasticity if stress is increased the ratio of stress to strain 

The unit of Young's modulus of elasticity is- 

An object of mass 'm' is suspended at the end of a mass-less wire of length L and area of cross-section A. Young's modulus of the maternal of the wire is Y. if the mass is pulled down slightly its freq. of oscillation along the vertical direction is :

There is no change in the volume of a wire due to a change in its length on stretching. The Poisson's ratio of the material of the wire is

Consider two cylindrical rods of identical dimensions, one of rubber and the other of steel. Both the rods are fixed rigidly at one end of the roof. A mass M is attached to each of the free ends at the centre of the rods. Then: