Question

A massless string of length l passes over a frictionless pulley with horizontal axis. Two monkeys hang from the ends of the string at the same distance l/2 from the pulley, the monkeys start climbing upwards simultaneously. First monkey climbs with a speed v relative to the string and the second with speed of 2v. Both monkeys have got same masses. The time taken by the first and second monkeys in reaching the pulleys are respectively.

• A. $\left( \frac { 1 } { \mathrm { v } } \right) , \left( \frac { 1 } { 2 \mathrm { v } } \right)$
• B. $\sqrt { \frac { 21 } { \mathrm { v } } }$ , $\sqrt { \frac { 1 } { \mathrm { v } } }$
• C. $\left( \frac { 1 } { 2 \mathrm { v } } \right) ^ { 1 / 2 } , \left( \frac { 1 } { \mathrm { v } } \right) ^ { 1 / 2 }$
• D. $\left( \frac { 1 } { 3 v } \right)$ , $\left( \frac { 1 } { 3 v } \right)$

Answer 1

Answer: (D)

$\left( \frac { 1 } { 3 v } \right)$ , $\left( \frac { 1 } { 3 v } \right)$

Answer 2

Relative velocity of monkeys = v + 2v = 3v

Total distance covered = $\frac { 1 } { 2 } +$ $\frac { 1 } { 2 }$ = l

∴ time taken by each monkey = $\frac { 1 } { 3 \mathrm { v } }$