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

Question

A 24 kg block resting on a floor has a rope tied to its top. The maximum tension, the rope can withstand without breaking is 310 N . The minimum time in which the block can be lifted a vertical distance of 4.6 m by pulling on the rope is (A) 1.2s (B) 1.3 s (C) 1.7 s (D) 2.3 s

Tardigrade Admin · Accepted Answer

Effective upward force = 310 -mg =310-24× 9.8=74.8 N Upward acceleration ∴ a = text74.8/24 = text3.12 m s- 2 As s=ut+(1/2)at2 4.6 =0+(1/2)× 3.12× t2 or t2=(4.6/1.56)=2.95 or t=√2.95=1.7 s

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

$1.2 s$

$1.3 s$

$1.7 s$

$2.3 s$

Effective upward force = 310 $- m g$
$= 310 - 24 \times 9.8 = 74.8$ N
Upward acceleration
$∴ a = 74.8/24 = 3.12 m s^{- 2}$
As $s = u t + \frac{1}{2} a t^{2}$
4.6 $= 0 + \frac{1}{2} \times 3.12 \times t^{2}$
or $t^{2} = \frac{4.6}{1.56} = 2.95$
or $t = 2.95 = 1.7$ s

Q. 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

1.2s

1.3s

1.7s

2.3s