Q. No.The edge of an aluminum cube is \(10~\text{cm}\) long. One face of the cube is firmly fixed to a vertical wall. A mass of \(100~\text{kg}\) is then attached to the opposite face of the cube. The shear modulus of aluminum is \(25~\text{GPa}.\) What is the vertical deflection of this face?
1. \(4.86 \times10^{-6}~\text m\)
2. \(3.92 \times 10^{-7}~\text m\)
3. \(3.01 \times10^{-6}~\text m\)
4. \(6.36 \times10^{-7}~\text m\)
1. \(4.86 \times10^{-6}~\text m\)
2. \(3.92 \times 10^{-7}~\text m\)
3. \(3.01 \times10^{-6}~\text m\)
4. \(6.36 \times10^{-7}~\text m\)
The average depth of the Indian Ocean is about \(3000~\text m.\) The fractional compression \(\frac{\Delta V}{V},\) of water at the bottom of the ocean is?
(Given that the bulk modulus of water is \(2.2\times10^{9}~\text{Nm}^{-2}\) and \(g=10~\text{ms}^{-2}\))
1. \(1.36\times10^{-3}\)
2. \(2.36\times10^{-3}\)
3. \(1.36\times10^{-2}\)
4. \(2.36\times10^{-2}\)
A rope \(1\) cm in diameter breaks if the tension in it exceeds \(500\) N. The maximum tension that may be given to a similar rope of diameter \(2\) cm is:
1. \(500\) N
2. \(250\) N
3. \(1000\) N
4. \(2000\) N
The length of a metal wire is \(l_1\) when the tension in it is \(T_1\) and is \(l_2\) when the tension is \(T_2.\) The natural length of the wire is:
| 1. | \(\dfrac{l_{1}+l_{2}}{2}\) | 2. | \(\sqrt{l_{1} l_{2}}\) |
| 3. | \(\dfrac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}}\) | 4. | \(\dfrac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}}\) |
A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break:
| 1. | when the mass is at the highest point |
| 2. | when the mass is at the lowest point |
| 3. | when the wire is horizontal |
| 4. | at an angle of \(\cos^{-1}\left(\dfrac{1}{3}\right)\) from the upward vertical |
When a metal wire elongates by hanging a load on it, the gravitational potential energy decreases.
| 1. | This energy completely appears as the increased kinetic energy of the block. |
| 2. | This energy completely appears as the increased elastic potential energy of the wire. |
| 3. | This energy completely appears as heat. |
| 4. | None of the above. |
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:
| 1. | \( \dfrac{x^2}{2 L^2} \) | 2. | \(\dfrac{x}{\mathrm{~L}} \) |
| 3. | \(\dfrac{x^2}{L}\) | 4. | \(\dfrac{x^2}{2L}\) |
The maximum load a wire can withstand without breaking when its length is reduced to half of its original length, will:
1. be doubled
2. be halved
3. be four times
4. remain the same
1. infinity
2. zero
3. unity
4. some finite small non-zero constant value
A wire of cross-section \(A_{1}\) and length \(l_1\) breaks when it is under tension \(T_{1};\) a second wire made of the same material but of cross-section \(A_{2}\) and length \(l_2\) breaks under tension \(T_{2}.\) A third wire of the same material having cross-section \(A,\) length \(l\) breaks under tension \(\dfrac{T_1+T_2}{2}.\) Then:
| 1. | \(A=\dfrac{A_1+A_2}{2},~l=\dfrac{l_1+l_2}{2}\) |
| 2. | \(l=\dfrac{l_1+l_2}{2}\) |
| 3. | \(A=\dfrac{A_1+A_2}{2}\) |
| 4. | \(A=\dfrac{A_1T_1+A_2T_2}{2(T_1+T_2)},~l=\dfrac{l_1T_1+l_2T_2}{2(T_1+T_2)}\) |
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