Wires W\(_1\) and W\(_2\) are made of same material having the breaking stress of 1.25\(\times\)10\(^9\) N/m\(^2\). W\(_1\) and W\(_2\) have cross-sectional area of 8\(\times\)10\(^{-7}\) m\(^2\) and 4\(\times\)10\(^{-7}\) m\(^2\), respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is _________ kg. (Use g = 10 m/s\(^2\))
A bullet of 10 g, moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m/s. The length of the pendulum is 0.5 m and mass of the bob is 1 kg. The minimum value of v = _________ m/s so that the pendulum describes a circle. (Assume the string to be inextensible and g = 10 m/s\(^2\))
The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use g = 10 m/s\(^2\)):
Match List - I with List - II. Choose the most appropriate answer from the options given below :
A rod CD of thermal resistance 10.0 KW\(^{-1}\) is joined at the middle of an identical rod AB as shown in figure. The ends A, B and D are maintained at 200\(^{\circ}\)C, 100\(^{\circ}\)C and 125\(^{\circ}\)C respectively. The heat current in CD is P watt. The value of P is _________.
The resultant of these forces \(\vec{OP}, \vec{OQ}, \vec{OR}, \vec{OS}\) and \(\vec{OT}\) is approximately ________ N. [Take \(\sqrt{3} = 1.7, \sqrt{2} = 1.4\). Given \(\hat{i}\) and \(\hat{j}\) unit vectors along x, y axis]