JEE Elasticity PYQs With Video Solutions, Download PDF

A wire fixed at the upper end stretches by length $$\ell$$ by applying a force $$F$$. The work done in stretching is

A wooden wheel of radius $$R$$ is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area $$S$$ and length $$L$$. $$L$$ is slightly less than $$2\pi R$$. To fit the ring on the wheel, it is heated so that its temperature rises by $$\Delta T$$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $$\alpha$$, and its Young's modulus is $$Y$$, the force that one part of the wheel applies on the other part is :

A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire is $$P \times 10^{11}$$ Nm$$^{-2}$$, where P is : (Take $$g = 3\pi$$ m/s$$^2$$)

Two wires as shown in the figure below, made of steel and have breaking stress of $$12 \times 10^8$$ N/m$$^2$$. Area of cross-section of upper wire is 0.008 cm$$^2$$ and of lower wire is 0.004 cm$$^2$$. The maximum mass that can be added to pan without breaking any wire is _______ kg. (take $$g = 10$$ m/s$$^2$$)

A uniform wire of length $$l$$ of weight w is suspended from the roof with a weight of W at the other end. The stress in the wire at $$\frac{l}{3}$$ distance from the top is $$\left(\frac{W}{A} + \frac{2}{\gamma} \cdot \frac{w}{A}\right)$$, where A is the cross sectional area of the wire. The value of $$\gamma$$ is __________.

A wire elongates by $$\ell\,mm$$ 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 $$mm$$)

The bulk moduli of ethanol, mercury and water are given as 0.9, 25 and 2.2 respectively in units of $$10^9$$ Nm$$^{-2}$$. For a given value of pressure, the fractional compression in volume is $$\frac{\Delta V}{V}$$. Which of the following statements about $$\frac{\Delta V}{V}$$ for these three liquids is correct?

When the temperature of a metal wire is increased from 0$$°$$C to 10$$°$$C, its length increases by 0.02%. The percentage change in its mass density will be closed to:

A uniform wire (Young's modulus $$2 \times 10^{11}$$ Nm$$^{-2}$$) is subjected to longitudinal tensile stress of $$5 \times 10^7$$ Nm$$^{-2}$$. If the overall volume change in the wire is 0.02%, the fractional decrease in the radius of the wire is close to:

If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will:

A string of area of cross-section 4 mm$$^2$$ and length 0.5 is connected with a rigid body of mass 2 kg. The body is rotated in a vertical circular path of radius 0.5 m. The body acquires a speed of 5 m s$$^{-1}$$ at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _____ $$\times 10^{-5}$$. (Use Young's modulus $$10^{11}$$ N m$$^{-2}$$ and $$g = 10 \ m s^{-2}$$)

Two wires A and B are made of same material having ratio of lengths $$\frac{L_A}{L_B} = \frac{1}{3}$$ and their diameters ratio $$\frac{d_A}{d_B} = 2$$. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45° with the load axis. The length of the wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be $$x \times 10^4$$ N m$$^{-2}$$. The value of $$x$$ is _____.

In an experiment with photoelectric effect, the stopping potential,

The increase in the pressure required to decrease the volume $$(\Delta V)$$ of water is $$6.3 \times 10^7$$ N/m². The percentage decrease in the volume is _____. (Bulk modulus of water = $$2.1 \times 10^9$$ N/m².)

The bulk modulus of a liquid is $$3 \times 10^{10}$$ Nm$$^{-2}$$. The pressure required to reduce the volume of liquid by $$2\%$$ is :

The Young's modulus of a steel wire of length $$6$$ m and cross-sectional area $$3$$ mm$$^2$$, is $$2 \times 10^{11}$$ N/m$$^2$$. The wire is suspended from its support on a given planet. A block of mass $$4$$ kg is attached to the free end of the wire. The acceleration due to gravity on the planet is $$\frac{1}{4}$$ of its value on the earth. The elongation of wire is (Take $$g$$ on the earth $$= 10$$ m/s$$^2$$):

a

Under the same load, wire A having length 5.0 m and cross section $$2.5 \times 10^{-5}$$ m$$^2$$ stretches uniformly by the same amount as another wire B of length 6.0 m and a cross section of $$3.0 \times 10^{-5}$$ m$$^2$$ stretches. The ratio of the Young's modulus of wire A to that of wire B will be:

A wire of length $$L$$ and radius $$r$$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $$f$$, its length increases by $$l$$. Another wire of same material of length $$2L$$ and radius $$2r$$ is pulled by a force $$2f$$. Then the increase in its length will be:

The length of a wire becomes $$l_1$$ and $$l_2$$ when 100 N and 120 N tension are applied respectively. If $$10l_2 = 11l_1$$, then the natural length of wire will be $$\frac{1}{x}l_1$$. Here the value of $$x$$ is _______

A metal string A is suspended from a rigid support and its free end is attached to a block of mass M. Second block having mass 2M is suspended at the bottom of the first block using a string B. The area of cross sections of strings A and B are same. The ratio of lengths of strings of A to B is 2 and the ratio of their Young's moduli $$(Y_A/Y_B)$$ is 0.5. The ratio of elongations in A to B is ______.

The Young's modulus of steel wire of radius $$r$$ and length $$L$$ is $$Y$$. If the radius $$r$$ and length $$L$$ of the wire are doubled then the value of $$Y$$

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is $$4 \times 10^8$$ N/m$$^2$$ and its radius is 4 mm, then maximum acceleration the lift can take is _______ m/s$$^2$$.
(take g = 10 m/s$$^2$$ and $$\pi$$ = 3.14)

A certain gas is isothermally compressed to $$\left(\frac{1}{3}\right)^{rd}$$ of its initial volume ($$V_0 = 3$$ litre) by applying required pressure. If the bulk modulus of the gas is $$3 \times 10^5$$ N/m$$^2$$, the magnitude of work done on the gas is _______ J.

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross-section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere $$\left(\frac{dr}{r}\right)$$, is:

A square aluminium (shear modulus is $$25 \times 10^9 \text{ N m}^{-2}$$) slab of side $$60 \text{ cm}$$ and thickness $$15 \text{ cm}$$ is subjected to a shearing force (on its narrow face) of $$18.0 \times 10^4 \text{ N}$$. The lower edge is riveted to the floor. The displacement of the upper edge is ______ $$\mu m$$.

A cube has side length 5 cm and modulus of rigidity $$10^5$$ N/m$$^2$$. The displacement produced by a force of 10 N in the upper face of cube is _______ mm.

A steel rod of length 1 m and cross-sectional area $$10^{-4}$$ m$$^2$$ is heated from 0$$^\circ$$C to 200$$^\circ$$C without being allowed to extend or bend. The compressive tension produced in the rod is _______ $$\times 10^4$$ N. (Given Young's modulus of steel $$= 2 \times 10^{11}$$ N m$$^{-2}$$, coefficient of linear expansion $$= 10^{-5}$$ K$$^{-1}$$)

Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area $$A$$ and wire-2 has cross-sectional area $$3A$$. If the length of wire 1 increases by $$\Delta x$$ on applying force $$F$$, how much force is needed to stretch wire 2 by the same amount?