Question

In the figure shown, the acceleration of wedge is (neglect friction):

Answer 1

Hint: To solve this problem find the forces acting on the wedge due to the applied force on the string using free body diagrams or Newton’s laws of motion. To find the forces and its component on the block use Newton’s second law which states that the net force acting on a system is equal to the mass times the acceleration of the system.

Formula used:
The Newton’s law is given by,
\[F = ma\]
where $m$ is the mass and a is the acceleration of the system.

Complete step by step answer:
We know that Newton's second law states that the total force acting on a body is equal to the mass times the acceleration of the system. So, here we have to find the force acting on the wedge due to the force on the string. We can do that easily by dividing the force acting into components and looking for any force acting on the wedge. So, if we draw the free body diagram we can see that,

\[F = T\]
Equation of motion of the block $m$.
\[T = F = ma\]
So, due to the force acting there is a tension in the string this tension will generate the same amount of force on the block kept horizontal. So, all of the forces are balanced and no component of forces are acting on the wedge. The force is acting only on the block and the string.

Hence, the total force acting on the wedge is zero.

Note:To solve this type of force problem just draw the force diagram or free body diagram of the system to find the required force which is acting. We can also find it by using Newton’s law of motion directly by mathematical derivation but for complicated problems that may lead to complicated calculations also. So, it is advised to use a force diagram to find the forces acting on the system or body rather easily.