Mechanical Prop...

A spiral spring is stretched to 20.5 cm gradation on a metre scale when loaded with a 100 g load and to the 23.3 cm gradation by 200 g load. The spring is used to support a lump of metal in air and the reading now is 24.0 cm. The mass of metal lump is :

A stone of mass m tied to one end of a thread of length l. The diameter of the thread is d and it is suspended vertically. The stone is now rotated in a horizontal plane and makes an angle $$\theta$$ with the vertical. Find the increase in length of the wire. Young's modulus of the wire is Y.

A steel cylindrical rod of length $$l$$ and radius $$r$$ is suspended by its end from the ceiling. Find the elastic deformation energy $$U$$ of the rod.

A uniform heavy rod of length $$L$$, weight $$W$$ and cross-sectional area $$A$$ is hanging from a fixed support. Young's modulus of the material is $$Y$$. Find the elongation of the rod.

Poisson's ratio cannot exceed

The length of a wire is $$l_1$$ when tension is $$T_1$$ and $$l_2$$ when tension is $$T_2$$. The natural length of the wire is

A sphere of mass M kg is suspended by a metal wire of length L and diameter d. When in equilibrium, there is a gap of $$\Delta l$$ between the sphere and the floor. The sphere is gently pushed aside so that it makes an angle $$\theta$$ with the vertical. Find $$\theta_{max}$$ so that sphere fails to rub the Floor, Young's modulus of the wire is Y.

A copper wire of cross-section A is under a tension T. Find the decrease in the cross-section area. Young's modulus is Y and Poisson's ratio is $$\sigma$$

Each wire in Fig. has cross-section area $$5\times10^{-3}cm^{2}$$ and $$Y=2\times10^{11}Pa$$. P, Q and R have mass $$3 kg$$ each. Find the strain developed in A. Assume surface to be smooth.

Young's modulus of rubber is $$10^{4} N/m^{2}$$ and area of cross section is $$2\ cm^{-2}$$. If force of $$2\times 10^{5}$$ dyn is applied along its length, then its initial $$l$$ becomes.