Question

System shown in figure is released from rest. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves contact with ground is : (Take force constant of spring k = 40 N/m and g = 10 m/s²)

• A. $\sqrt { 2 }$ m/s
• B. $2 \sqrt { 2 }$ m/s
• C. 2 m/s
• D. $4 \sqrt { 2 }$ m/s

Answer 1

Answer: (B)

$2 \sqrt { 2 }$ m/s

Answer 2

Let x be the extension is spring when 2 kg block leaves the contact with ground. Then kx = 2g

x = $\frac { 2 \mathrm {~g} } { \mathrm { k } }$ = $\frac { 2 \times 10 } { 40 }$ = $\frac { 1 } { 2 } \mathrm {~m}$

Now from conservation of energy,

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

̃ v = $\sqrt { 2 \mathrm { gx } - \frac { \mathrm { kx } ^ { 2 } } { \mathrm {~m} } }$ = $2 \sqrt { 2 } \mathrm {~m} / \mathrm { s }$