Eight drops of equal radii are falling through air with a steady velocity of \(3\text{ cm/s}\). If the eight drops combine to form a single drop, then its steady velocity will be
1. \(3\text{ cm/s}\)
2. \(12\text{ cm/s}\)
3. \(6\text{ cm/s}\)
4. \(24\text{ cm/s}\)
View Answer
Terminal velocity \(v \propto r^2\). Since volume remains constant, \(\frac{4}{3}\pi R^3 = 8 \times \frac{4}{3}\pi r^3 \implies R = 2r\). Thus, the new terminal velocity is \(v' = \left(\frac{R}{r}\right)^2 v = 2^2 \times 3 = 12\text{ cm/s}\).
The experiment which is used to determine Young’s modulus of the material of a given wire, is
1. Resonance tube experiment
2. Displacement method
3. Searle's experiment
4. Young's double slit experiment
View Answer
Searle's apparatus/experiment is specifically designed and used to determine the Young's modulus of elasticity of a metal wire by measuring elongation under load.
Experimental observations show that for given solid material, the magnitude of strain produced is same whether the stress is tensile or compressive. The ratio of tensile stress to longitudinal strain is defined as Young’s modulus and is denoted by \(Y = \sigma/e\). The length of a metal wire is \(l_A\) when the tension in it is \(T_A\) and is \(l_B\) when tension is \(T_B\). The natural length of wire is
1. \[\frac{T_B l_B + T_A l_A}{T_A + T_B}\]
2. \[\frac{T_B l_B - T_A l_A}{T_A - T_B}\]
3. \[\frac{T_B l_A - T_A l_B}{T_B - T_A}\]
4. \[\frac{T_B l_B + T_A l_A}{T_A - T_B}\]
View Answer
Let the natural length be \(L\). Using Hooke's law, \[l_A = L(1 + T_A/AY)\] and \[l_B = L(1 + T_B/AY)\]. Eliminating \(AY\) gives \[L = \frac{T_B l_A - T_A l_B}{T_B - T_A}\].