Question

Same current flows through both the left and the right arms, and the legs of the robot.

Given:
Current = $x$ ampere
Left arm force = 7$x$ - 15/2 N
Right arm force = 14($x$/2 - 15/28) N

From the data above, choose the correct statement from the following:

• A. The force is balanced for all values of the current.
• B. The force is unbalanced for all value of $x$.
• C. The force is balanced for specific values of $x$.
• D. Cannot be determined

Answer 1

The correct option is A The force is balanced for all values of the current.

Given:
Current = $x$ ampere
Left arm force = 7$x$ - 15/2 N
Right arm force = 14($x$/2 - 15/28) N

To find the value of current for which the force produced by both the arms are equal, let's equate the expressions given.

So,
7$x$ + (-15/2) = 14($x$/2 - 15/28)
$\Rightarrow$ 7$x$ + (-15/2) = 7$x$ + (-15/2)
$\Rightarrow$ 7$x$ + (-15/2) + (-7$x$) + 15/2 = 0
$\Rightarrow$ 7$x$ + (-7$x$) + 15/2 + (-15/2) = 0 [by commutative property]
$\Rightarrow$ {7$x$ - 7$x$} + {15/2 - 15/2} = 0 [by associative property]
$\Rightarrow$ 0 = 0 [This is true for all values of $x$.]

Hence, the force is balanced for all values of the current.