Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is :

The actual value of resistance R, shown in the figure is 30$$\Omega $$. This is measuered in an experiment as shown using the standard formula R = $${V \over {\rm I}}$$, where V and I are the readings of the voltmeter and ammeter, respectively. If the measured value of R is 5% less, then the internal resistance of the voltmeter is -

The Wheatstone bridge shown in figure, here, gets balanced when the carbon resistor used as R₁ has the colour code (Orange, Red, Brown). The resistors R₂ and R₄ are 80$$\Omega $$ and 40$$\Omega $$, respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as R₃, would be -

A particle starts from the origin at time t = 0 and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time t = 5s ?