Physics — mixed

Under isothermal condition, the pressure of a gas is given by $$\mathrm{P}=a \mathrm{~V}^{-3}$$, where $$a$$ is a constant and $$\mathrm{V}$$ is the volume of the gas. The bulk modulus at constant temperature is equal to

Young's moduli of the material of wires A and B are in the ratio of $$1: 4$$, while its area of cross sections are in the ratio of $$1: 3$$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires $$\mathrm{A}$$ and $$\mathrm{B}$$ will be in the ratio of [Assume length of wires A and B are same]

An aluminium rod with Young's modulus $$Y=7.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$$ undergoes elastic strain of $$0.04 \%$$. The energy per unit volume stored in the rod in SI unit is:

With rise in temperature, the Young's modulus of elasticity :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity. Reason (R) : The restoring force depends upon the bonded inter atomic and inter molecular force of solid. In the light of the above statements, choose the correct answer from the options given below :

A ball is projected with kinetic energy E, at an angle of $$60^{\circ}$$ to the horizontal. The kinetic energy of this ball at the highest point of its flight will become :

A wire of length $$L$$ and radius $$r$$ is clamped at one end. If its other end is pulled by a force $$F$$, its length increases by $$l$$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

Young's modules of material of a wire of length '$$L$$' and cross-sectional area $$A$$ is $$Y$$. If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be :

Young's modulus is determined by the equation given by $$\mathrm{Y}=49000 \frac{\mathrm{m}}{\mathrm{l}} \frac{\mathrm{dyne}}{\mathrm{cm}^2}$$ where $$M$$ is the mass and $$l$$ is the extension of wire used in the experiment. Now error in Young modules $$(Y)$$ is estimated by taking data from $$M-l$$ plot in graph paper. The smallest scale divisions are $$5 \mathrm{~g}$$ and $$0.02 \mathrm{~cm}$$ along load axis and extension axis respectively. If the value of $M$ and $l$ are $$500 \mathrm{~g}$$ and $$2 \mathrm{~cm}$$ respectively then percentage error of $$Y$$ is :

Match List I with List II : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} LIST I LIST II A. A force that restores an elastic body of unit area to its original state I. Bulk modulus B. Two equal and opposite forces parallel to opposite faces II. Young's modulus C. Forces perpendicular everywhere to the surface per unit area same everywhere III. Stress D. Two equal and opposite forces perpendicular to opposite faces Choose the correct answer from the options given below : IV. Shear modulus Choose the correct answer from the options given below :