The maximum load a wire can withstand without breaking, when its length is reduced to half of its original length, will:

The stress-strain graphs for two materials are: (assume same scale).

A wire is suspended from the ceiling and stretched under the action of a weight F suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight. Which of the following options is correct?

Modulus of rigidity of ideal liquids is:

The modulus of rigidity of the ideal liquid is:

Q.2 The maximum load a wire can withstand without breaking when its length is reduced to half of its original length, will:

Q.3 The temperature of the wire is doubled. Young's modulus of elasticity:

Q.4 A spring is stretched by applying a load to its free end. The strain produced in the spring is:

Q.5 A rigid bar of mass M is supported symmetrically by three wires each of length l. Those at each end are of copper and the middle one is of iron. The ratio of their diameters, if each is to have the same tension, is equal to:

A mild steel wire of length 2L and cross-sectional area A is stretched, well within the elastic limit, horizontally between two pillars (figure). A mass m is suspended from the mid-point of the wire. Strain in the wire is:

Q.7 A rectangular frame is to be suspended symmetrically by two strings of equal length on two supports (figure). It can be done in one of the following three ways;

The tension in the strings will be

Q.8 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.

The figure given below shows the longitudinal stress vs longitudinal strain graph for a given material. Based on the given graph, Young's modulus of the material with the increase in strain will:

Q.9 The stress-strain graphs for two materials are shown in figure. (assumed same scale)

(a) Material (ii) is more elastic than material (i) and hence material (ii) is more brittle

(b) Material (i) and (ii) have the same elasticity and the same brittleness

(c) Material (ii) is elastic over a larger region of strain as compared to (i)

(d) Material (ii) is more brittle than material (i)

Q.10 A wire is suspended from the ceiling and stretched under the action of a weight F suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight.

(a) Tensile stress at any cross-section A of the wire is F/A.

(b) Tensile stress at any cross-section is zero.

(c) Tensile stress at any cross-section A of the wire is 2F/A.

(d) Tension at any cross-section A of the wire is F.

Q. 11 A rod of length l and negligible mass is suspended at its two ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths (figure). The cross-sectional areas of wires A and B are $1.0 {\mathrm{mm}}^2 \mathrm{and} 2.0 {\mathrm{mm}}^2$ respectively. (${\mathrm{Y}}_{\mathrm{Al}}=70\times {10}^9 \mathrm{N}/{\mathrm{m}}^2 \mathrm{and} {\mathrm{Y}}_{\mathrm{steel}}=200\times {10}^9 \mathrm{N}/{\mathrm{m}}^2$)

(a) Mass m should be suspended close to wire A to have equal stresses in both the wires.

(b) Mass m should be suspended close to B to have equal stresses in both the wires.

(c) Mass m should be suspended at the middle of the wires to have equal stresses in both the wires.

(d) Mass m should be suspended close to wire A to have equal strain in both wires.

Q.12 For an ideal liquid,

(a) The bulk modulus is infinite

(b) The bulk modulus is zero

(c) The shear modulus is infinite

(d) The shear modulus is zero

Q. 13 A copper and a steel wire of the same diameter are connected end to end. A deforming force F is applied to this composite wire which causes a total elongation of 1 cm. The two wires will have

1. The same stress

2. Different stress

3. The same strain

4. Different strain

A structural steel rod has a radius of 10 mm and a length of 1.0 m. A 100 kN force stretches it along its length. The stress produced and the elongation in the rod, respectively, are?

(Young’s modulus of structural steel is $2.0\times {10}^{11} {\mathrm{Nm}}^{-2}.$)

A copper wire of length 2.2 m and a steel wire of length 1.6 m, both of diameter 3.0 mm, are connected end to end. When stretched by a load, the net elongation is found to be 0.70 mm. The load applied is:

$\left({\mathrm{Y}}_{\mathrm{C}} = 1.1\times {10}^{11} \mathrm{N} {\mathrm{m}}^2 \mathrm{and} {\mathrm{Y}}_{\mathrm{S}} = 2.0\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}\right)$

In a human pyramid in a circus, the entire weight of the balanced group is supported by the legs of a performer who is lying on his back (as shown in the figure below). The combined mass of all the persons performing the act, and the tables, plaques, etc. involved is 280 kg. The mass of the performer lying on his back at the bottom of the pyramid is 60 kg. Each thighbone (femur) of this performer has a length of 50 cm and an effective radius of 2.0 cm. The amount by which each thighbone gets compressed under the extra load is:

(The Young’s modulus for bone is given by, Y = $9.4\times {10}^9 \mathrm{N} {\mathrm{m}}^{-2}$)

A square lead slab of side 50 cm and thickness 10 cm is subject to a shearing force (on its narrow face) of $9.0\times {10}^4 \mathrm{N}$. The lower edge is riveted to the floor as shown in the figure below. How much will the upper edge be displaced?

$\left(\mathrm{Shear} \mathrm{modulus} \mathrm{of} \mathrm{lead} = 5.6\times {10}^9 \mathrm{N} {\mathrm{m}}^{-2}\right)$

The average depth of the Indian Ocean is about 3000 m. The fractional compression, ∆V/V, of water at the bottom of the ocean is? Given that the bulk modulus of water is $2.2\times {10}^9 {\mathrm{Nm}}^{-2}.$

(Take $\mathrm{g} = 10 \mathrm{m} {\mathrm{s}}^{-2}$)