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 $\mathrm { g } = 10 \mathrm {~ms} ^ { - 2 }$ )

• A. The monkey climbs up with an acceleration of $5 \mathrm {~ms} ^ { - 2 }$
• B. The monkey climbs down with an acceleration of $5 \mathrm {~ms} ^ { - 2 }$
• C. The monkey climbs up with a uniform speed of $5 \mathrm {~ms} ^ { - 2 }$
• D. The monkey falls down the rope freely under gravity

Answer 1

Answer: (A)

The monkey climbs up with an acceleration of $5 \mathrm {~ms} ^ { - 2 }$

Answer 2

Here mass of monkey m = 40kg

Maximum tension the rope can stand T = 500N

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 $a = 5 \mathrm {~ms} ^ { - 2 }$

$R = m ( g + a ) = 40 ( 10 + 5 ) = 600 \mathrm {~N}$

R>T

Hence the roe will break

(2) When the monkey climbs down with an acceleration

$a = 5 \mathrm {~ms} ^ { - 2 }$

$R = m ( g - a ) = 40 ( 10 - 5 ) = 200 \mathrm {~N}$

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

$\therefore R = m g = 40 \times 10 = 400 \mathrm {~N}$

R<T

Hence the rope will not break

(4) When the monkey falls down the rope freely under gravity $a = g$

$\therefore R = m g ( g - a ) = m ( g - g ) =$ zero

Hence the rope will not break