Question

A $24kg$ block resting on a floor has a rope tied to its top. The maximum tension the rope can withstand without breaking is $310N$. The minimum time in which the block can be lifted a vertical distance of $4.6m$ by pulling on the rope is

• A. $1.2s$
• B. $1.3s$
• C. $1.7s$
• D. $2.3s$

Answer 1

The correct option is C

$1.7s$

Step 1: Given Data

Mass of the block $m=24kg$

Maximum tension on the rope $T=310N$

Height at which the block is to be lifted $h=4.6m$

Let the acceleration in the upward direction be $a$.

Let the acceleration due to gravity be $g=10m/s^2$.

Step 2: Calculate the Acceleration

The tension acts in the upward direction and the weight of the block acts in the downward direction.

Therefore, the equation of motion can be written as,

$T-mg=ma$

$\Rightarrow T=m\left(g+a\right)$

Upon substituting the values we get,

$310=24\left(10+a\right)$

$\Rightarrow a=\frac{310}{24}-10$

$\Rightarrow a=\frac{35}{12}m/s^2$

Step 3: Calculate the time taken

According to Newton's second equation of motion,

$S=ut+\frac{1}{2}a{t}^2$

Since the initial velocity is zero, the equation can be rewritten as,

$h=\frac{1}{2}a{t}^2$

$\Rightarrow t=\sqrt{\frac{2h}{a}}$

Upon substituting the values we get,

$t=\sqrt{\frac{2\times 4.6\times 12}{35}}=1.7s$

Hence, the correct answer is option (C).