Solving the pulley problem without writing the force equations

00:56 Hint given | 01:59 Solution starts | 06:35 Tension | 08:53 Acceleration of COM

Question N1L1: Concepts used in solution

Acceleration due to gravity | Center of mass | Vectors

Solving the pulley problem by writing the force equations by MIT OCW

Problem statement

Without writing the force equations, find the acceleration (a) of mass m in the pulley system shown in the figure. Reason the dependence of acceleration on the given masses m, M and acceleration due to gravity g by varying their values and comparing with known limits. Also, use the symmetries in the problem. Assume the pulley and rope to be massless and surfaces frictionless. Similarly, find tension T in rope and A the acceleration of the center of mass of m and M.

What is the direction of the electric field inside a charged hemispherical shell?

Video solution to electric field inside charged hemispherical shell

Question ES1L1: Concepts used in solution

Shell theorem | Superposition principle | Vector addition

Problem statement

The electric field at point P(0,y) inside a positively charged hemispherical shell of radius R, is given to be E. What is the field at the point Q(0, -y)? What is the direction of the y-component of the electric field at any general point G inside the hemisphere? What is the direction of the horizontal component of the electric field at any point B on the base surface?