A small block of mass m is kept on a rough inclined surface of inclination `theta` fixed in an elevator. The elevator goes up with a uniform velocity v and te block does not slide n te wedge. The work done by the force of friction on the block in time t will be

Options

A. zero
B. `mgvt cos^2theta`
C. mgvt sin^2theta`
D. `mgvt si 2theta`

Answer

To solve the problem step by step, we need to analyze the forces acting on the block and the work done by the friction force as the elevator moves upward with a constant velocity.

### Step 1: Understand the Forces Acting on the Block
1. The block of mass \( m \) is on an inclined surface with an angle \( \theta \).
2. The gravitational force acting on the block is \( mg \), where \( g \) is the acceleration due to gravity.
3. The gravitational force can be resolved into two components:
- Perpendicular to the incline: \( mg \cos \theta \)
- Parallel to the incline: \( mg \sin \theta \)