Question

Cube A is suspended by a string that passes over an ideal pulley and is tied to cube B, which is on a level horizontal frictionless table, as shown. Engineers are to determine the mass of cube B from the motion of the two-cube system after it is released from rest.They plan to measure the time cube A takes to reach the floor.The engineers must also take which of the following measurements to determine the mass of cube B?Question 7 options:The length of the string and the distance cube A falls to reach the floorThe mass of cube A and the distance cube A falls to reach the floorOnly the mass of cube AOnly the distance cube A falls to reach the floorOnly the length of the stringThe mass of cube A and the length of the string

Answer 1

The correct answer is 2nd option: The mass of cube A and the distance cube A falls to reach the floor

Explanation:

Final velocity for cube A after reaching on floor its equal to 0 (v = 0)

The change in potential energy provides kinetic energy for the motion of cube B, therefore:

`\begin{gathered} PE=M_A\cdot g\cdot h \\ \\ (1)/(2)M_B(v)^2=(1)/(2)M_B(u)^2 \end{gathered}`

The value of v as mentioned above is equal to 0, therefore we must calculate the value u, using the following formula:

`\begin{gathered} h=(-u)/(2g) \\ \\ u=(-h\cdot2g) \end{gathered}`

So we would finally be left with the following equation:

`M_A\cdot g\cdot h=(1)/(2)\cdot M_B(-h\cdot2g)^2`

This means that if we know the mass of A and the distance cube A falls to reach the floor, we can calculate the mass of cube B.

The correct answer is 2nd option: The mass of cube A and the distance cube A falls to reach the floor