Question

Blocks A and B of masses m and 2m, respectively, are connected by a light string and are pulled along a horizontal surface of negligible friction by a horizontal force of magnitude F, as shown in the figure. The tension in the string is T. If the masses of the blocks are doubled, and the magnitude of the horizontal force remains the same, the tension in the string will be:
a) 1/4T
b) 1/2T
c) T
d) 2T
e) 4T

Answer 1

When the masses of the blocks are doubled and the force applied is constant, the tension in the string will be the same.

The given parameters:

• Mass of block A = m
• Mass of block B = 2m
• Applied horizontal force, = F
• Tension in the string, = T

The acceleration of the blocks is calculated as follows;

$a = \frac{F}{m + 2m} \\\\a = \frac{F}{3m}$

The tension in the string is calculated as follows;

$T = ma\\\\T = m(\frac{F}{3m)}\\\\T= \frac{F}{3}$

When the masses of the blocks are doubled and the force applied is constant;

$a = \frac{F}{2m + 4m} \\\\a = \frac{F}{6m}$

The new tension in the string is calculated as follows;

$T_2 = ma\\\\T_2 = (2m) (\frac{F}{6m} )\\\\T_2 = \frac{F}{3} = T$

Thus, when the masses of the blocks are doubled and the force applied is constant, the tension in the string will be the same.

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