A monkey of mass 40 kg climbs on a massless rope which can stand a maximum tension of 500 N. In which of the following cases will the rope break (Take g = 10 $m s^{- 2}$ )

Question

A monkey of mass 40 kg climbs on a massless rope which can stand a maximum tension of 500 N. In which of the following cases will the rope break? (Take g = 10 $m s^{- 2}$ )

Smart Achievers · Accepted Answer

(1)

Here, mass of monkey, $m = 40 kg$

Maximum tension the rope can stand, $T = 500 N$

Tension in the rope will be equal to apparent weight of the monkey $(R)$ .

The rope will break when $R$ exceeds $T$ .

(1) When the monkey climbs up with an acceleration $a = 5 {m s}^{- 2}$

$R = m (g + a) = 40 (10 + 5) = 600 N$ $∴$ $R > T$

Hence, the rope will break.

(2) When the monkey climbs down with an acceleration $a = 5 {m s}^{- 2}$

$R = m (g - a) = 40 (10 - 5) = 200 N$ $∴$ $R < T$

Hence, the rope will not break.

(3) When the monkey climbs up with a uniform speed $v = 5 {m s}^{- 1}$ , its acceleration $a = 0$ .

$∴$ $R = m g = 40 \times 10 = 400 N$ $∴$ $R < T$

Hence, the rope will not break.

(4) When the monkey falls down the rope freely under gravity,

$a = g$ $∴$ $R = m (g - a) = m (g - g) = 0$

Hence, the rope will not break.

Solution

Q.
A monkey of mass 40 kg climbs on a massless rope which can stand a maximum tension of 500 N. In which of the following cases will the rope break (Take g = 10 $m s^{- 2}$ )

1 The monkey climbs up with an acceleration of 5 $m s^{- 2}$ .

2 The monkey climbs down with an acceleration of 5 $m s^{- 2}$ .

3 The monkey climbs up with a uniform speed of 5 $m s^{- 1}$ .

4 The monkey falls down the rope freely under gravity.

Want Us to Email you About Special Offers & Updates?

Solution

Q. A monkey of mass 40 kg climbs on a massless rope which can stand a maximum tension of 500 N. In which of the following cases will the rope break (Take g = 10 m s-2)

1 The monkey climbs up with an acceleration of 5 m s-2.

2 The monkey climbs down with an acceleration of 5 m s-2.

3 The monkey climbs up with a uniform speed of 5 m s-1.

4 The monkey falls down the rope freely under gravity.

Want Us to Email you About Special Offers & Updates?

Q.
A monkey of mass 40 kg climbs on a massless rope which can stand a maximum tension of 500 N. In which of the following cases will the rope break (Take g = 10 $m s^{- 2}$ )

1 The monkey climbs up with an acceleration of 5 $m s^{- 2}$ .

2 The monkey climbs down with an acceleration of 5 $m s^{- 2}$ .

3 The monkey climbs up with a uniform speed of 5 $m s^{- 1}$ .