There are two wire of same material and same length while the diameter of second wire is two times the diameter of first wire, then the ratio of extension produced in the wires by applying same load will be

1 : 1
2 : 1
1 : 2
4 : 1

Solution

A 2 m long rod of radius 1 cm which is fixed from one end is given a twist of 0.8 radian. The shear strain developed will be

0.002
0.004
0.008
0.016

Solution

\(\phi =\frac{r\theta }{\iota }=\frac{1}{100}\times \frac{0.8}{2}=0.004\, radian\)

Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will

increase
decrease
remain same
decrease for some, while increase for others

Solution

The molecular kinetic energy increases, and so termperature increases.

A metal rod of Young’s modulus 2 × 10¹⁰ N m^–2 undergoes an elastic strain of 0.06%. The energy per unit volume stored in J m^–3 is

3600
7200
10800
14400

Solution

U /volume = ¹⁄₂ Y × strain²= 3600 J m^–3

[Strain = 0.06 × 10^-2]

The length of a metal is l₁ when the tension init is T₁ and is l₂ when the tension is T₂. The original length of the wire is

\(\frac{\iota _{1}+ \iota _{2}}{2}\)
\(\frac{\iota _{1}T_{2}+ \iota _{2}T_{1}}{T_{1}+T_{2}}\)
\(\frac{\iota _{1}T_{2}- \iota _{2}T_{1}}{T_{1}-T_{2}}\)
\(\sqrt{T_{1}T_{2}\iota _{1}\iota _{2}}\)

Solution

A steel wire of length 20 cm and uniform cross-section 1 mm² is tied rigidly at both the ends. The temperature of the wire is altered from 40ºC to 20ºC. Coefficient of linear expansion for steel a= 1.1 × 10^–5/ºC and Y for steel is 2.0 × 10¹¹N/m². The change in tension of the wire is

2.2 × 10⁶ newton
16 newton
8 newton
44 newton

Solution

F= Y A ∝ t = (2.0 × 10¹¹) (10^–6) (1.1 × 10^–5) (20)= 44 newton

Two rods A and B of the same material and length have their radii r₁ and r₂ respectively. When they are rigidly fixed at one end and twisted by the same couple applied at the other end, the ratio \(\left ( \frac{Angle\, of\, twist\, at\, the\, end\, of\, A}{Angle\, of\, twist\, at\, the\, end\, of\, B} \right )\) is

\(r_{1}^{2}/r_{2}^{2}\)
\(r_{1}^{3}/r_{2}^{3}\)
\(r_{2}^{4}/r_{1}^{4}\)
\(r_{1}^{4}/r_{2}^{4}\)

Solution

The Young’s modulus of brass and steel are respectively 10¹⁰N/m². and 2 × 10¹⁰N/m². A brass wire and a steel wire of the same length are extended by 1 mm under the same force,the radii of brass and steel wires are R_B and R_S respectively. Then

R_S = √2 R_B
R_S = R_B/√2
R_S = 4R_B
R_S = R_B/4

Solution

A body of mass 10 kg is attached to a wire of radius 3 cm. It’s breaking stress is 4.8 × 10⁷ Nm^–2, the area of cross-section of the wire is 10^–6 m². What is the maximum angular velocity with which it can be rotated in the horizontal circle ?

1 rad sec^–1
2 rad sec^–1
4 rad sec^–1
8 rad sec^–1

Solution

Two wires of same material and length but cross-sections in the ratio 1 : 2 are used to suspend the same loads. The extensions in them will be in the ratio

1 : 2
2 : 1
4 : 1
1 : 4

Solution

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