Question

The pulley shown in fig. has radius 20 cm and MOI 0.2 kg m². Spring used has force constant 50 Nm^-1. The system is released from rest. Find the velocity of 1kg block when it has descended 10 cm.

• A. 1/2 ms^-1
• B. 1/√2 ms^-1
• C. 1/√3 ms^-1
• D. None

Answer 1

Answer: (A)

1/2 ms^-1

Answer 2

mgx = $\frac { 1 } { 2 }$kx² + $\frac { 1 } { 2 }$Iω² + $\frac { 1 } { 2 }$ mv²

1(10) (.1) = $\frac { 1 } { 2 }$ $\left[ 50 ( .1 ) ^ { 2 } + ( .2 ) \left( \frac { \mathrm { v } } { .2 } \right) ^ { 2 } + 1 \left( \mathrm { v } ^ { 2 } \right) \right]$

⇒ 2 = 0.5 + 6 v²

or v = 1/2 ms^-1