Concepts Of Physics MCQ Edition [Volume 1]PhysicsPhysics and Mathematics
A rod of length L is positioned along the X-axis between x = 0 and x = L . The linear density (mass/length) of the rod varies with the distance x from the origin as = a + bx . Determine the mass of the rod in terms of a , b and L .
Options
- AaL + bL^2 2
- BaL^2 2 + bL^3 3
- CaL + bL^2
- DaL 2 + bL^2 3
Correct answer
A. aL + bL^2 2
Step-by-step solution
The mass of the rod is given by the integral of the linear mass density over its length. M = ₀^ L , dx Substituting the given expression for : M = ₀^ L (a + bx) , dx M = [ ax + bx^2 2 ]₀^ L M = aL + bL^2 2