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 \(280~\text{kg}\). The mass of the performer lying on his back at the bottom of the pyramid is \(60~\text{kg}\). Each thighbone (femur) of this performer has a length of \(50~\text{cm}\) and an effective radius of \(2.0~\text{cm}\). The amount by which each thighbone gets compressed under the extra load is: (The Young’s modulus for bone is given by, \(Y = 9.4\times 10^9~\text{N/m}^{2}\))

1. \(4.55\times 10^{-5}~\text{cm}\)
2. \(5.45\times 10^{-3}~\text{cm}\)
3. \(5.45\times 10^{-5}~\text{cm}\)
4. \(4.55\times 10^{-3}~\text{cm}\)

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? Shear $\mathrm{modulus}$ $\mathrm{of}$ $\mathrm{lead}$ $=$ $5.6\times {10}^9$ $\mathrm{N}$ ${\mathrm{m}}^{-\mathrm{2 }}$

1.   0.16 mm

2.   1.8 mm

3.   18 mm

4.   16 mm

The average depth of the Indian Ocean is about \(3000\) m. The fractional compression, \(\frac{\Delta V}{V},\) of water at the bottom of the ocean is?
(Given that the bulk modulus of water is \(2.2\times10^{9}\) Nm^-2 and \(g=10\) ms^-2)
1. \(1.36\times10^{-3}\)
2. \(2.36\times10^{-3}\)
3. \(1.36\times10^{-2}\)
4. \(2.36\times10^{-2}\)

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:

1. be variable.

2. first increase & then decrease.

3. first decrease & then increase.

4. remain constant.

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:

Y_C  = 1.1 × 10¹¹ N m² and Y_S = 2.0 × 10¹¹ N m^-2
1.   $1.8\times {10}^2 \mathrm{N}$

2.   $1.8 \mathrm{N}$

3.   $1.8\times {10}^3 \mathrm{N}$

4.   $18\times {10}^3 \mathrm{N}$

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 $2.0\times {10}^{11} {\mathrm{Nm}}^{-2}.$)

1.   $3.18\times {10}^7 {\mathrm{Nm}}^{-2} \& 2.59 \mathrm{mm}$

2.   $3.18\times {10}^8 {\mathrm{Nm}}^{-2} \& 1.59 \mathrm{m}$

3.   $3.18\times {10}^8 {\mathrm{Nm}}^{-2} \& 1.59 \mathrm{mm}$

4.   $3.18\times {10}^7 {\mathrm{Nm}}^{-2} \& 2.59 \mathrm{m}$

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:

Choose the correct option:

For an ideal liquid,

Choose the correct option:

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. (${\mathrm{Y}}_{\mathrm{Al}}=70\times {10}^9 \mathrm{N}/{\mathrm{m}}^2 \mathrm{and} {\mathrm{Y}}_{\mathrm{steel}}=200\times {10}^9 \mathrm{N}/{\mathrm{m}}^2$)

The correct statements are:

1. (b, c)

2. (a, d)

3. (b, d)

4. (c, d)

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.
 

The correct statements are:
1. (a), (b)
2. (a), (d)
3. (b), (c)
4. (a), (c)