Which one of the following can completely balance several masses revol...
Explanation:
To balance several masses revolving in different planes on a shaft, it is necessary to introduce counterbalances that generate forces and moments to eliminate the unbalance. The counterbalances should be strategically placed to ensure that the resultant forces and moments in all planes are zero.
Option Analysis:
Let's analyze each option to determine whether it can completely balance the masses revolving in different planes on a shaft.
a) A single mass in one of the planes of the revolving masses:
This option will not completely balance the masses because it only introduces a counterbalance in one plane, neglecting the unbalance in the other planes. Therefore, option 'a' is not correct.
b) A single mass in a different plane:
Similarly, this option will not completely balance the masses as it only introduces a counterbalance in one plane, leaving the unbalance in the other planes. Hence, option 'b' is not correct.
c) Two masses in any two planes:
This option involves introducing two counterbalances in any two planes. By doing so, the forces and moments generated by the counterbalances can be adjusted to balance the revolving masses in all planes. This option is correct as it ensures complete balance by considering the unbalance in all planes.
d) Two equal masses in any two planes:
Although this option introduces two counterbalances, it does not guarantee complete balance unless the masses are equal and properly positioned. If the masses are not equal or not placed correctly, the unbalance in some planes may still exist. Therefore, option 'd' is not correct.
Conclusion:
From the analysis, it can be concluded that option 'c' is the correct answer. By introducing two masses in any two planes, it is possible to completely balance several masses revolving in different planes on a shaft.
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