Question

The maximum acceleration with which a body of mass 200 kg is lowered into a well using a rope having a breaking force of 50 kg-wt is (Acceleration due to gravity = 10 $ ms^{-2} $)

• A. $7.5 \, ms^{-2}$
• B. $5 \, ms^{-2}$
• C. $3 \, ms^{-2}$
• D. $2.5 \, ms^{-2}$

Hint:

When dealing with maximum or minimum acceleration under a constraint (like breaking force), consider the limiting value of the force.

Answer 1

The Correct Option is A

Step 1: Convert breaking force to Newtons.
$T_{max} = 50 \, kg-wt = 50 \times 10 \, N = 500 \, N$
Step 2: Apply Newton's second law.
When lowering the body with acceleration $a$, the net downward force is $mg - T = ma$.
Step 3: For maximum acceleration, tension is maximum (breaking force). $mg - T_{max} = ma_{max}$
Step 4: Substitute the given values.
$(200 \, kg)(10 \, ms^{-2}) - 500 \, N = (200 \, kg) a_{max}$ $2000 \, N - 500 \, N = 200 \, kg \times a_{max}$ $1500 \, N = 200 \, kg \times a_{max}$
Step 5: Solve for maximum acceleration.
$a_{max} = \frac{1500 \, N}{200 \, kg} = 7.5 \, ms^{-2}$
Thus, the maximum acceleration is $ \boxed{7.5 \, ms^{-2}} $.