Question

A knife of mass 1 kg slides on a frictionless wedge of mass 5 kg between two frictionless guides. At the instant shown in figure, the spring has initial compression 1m. Ground is also frictionless. Velocity of wedge when knife is about to touch the ground is (assume spring is ideal for large compressions)–

• A. $\frac { 6 } { \sqrt { 89 } } \mathrm {~m} / \mathrm { s }$
• B. $\frac { 12 } { \sqrt { 89 } } \mathrm {~m} / \mathrm { s }$
• C. $\frac { 2 } { \sqrt { 89 } } \mathrm {~m} / \mathrm { s }$
• D. $\frac { 24 } { \sqrt { 89 } } \mathrm {~m} / \mathrm { s }$

Answer 1

Answer: (D)

$\frac { 24 } { \sqrt { 89 } } \mathrm {~m} / \mathrm { s }$

Answer 2

By conservation of mechanical energy

1 × 10 × 3 + $\frac { 1 } { 2 }$ × 1 × 1² = $\frac { 1 } { 2 }$ × 1 × $\left( \frac { 3 } { 4 } \mathrm { v } _ { \mathrm { w } } \right) ^ { 2 }$ + $\frac { 1 } { 2 }$ × 5 × $\mathrm { v } _ { \mathrm { w } } ^ { 2 }$ + $\frac { 1 } { 2 } \times 1$ × 5²

(v_w : velocity of wedge)

̃ v_w = $\frac { 24 } { \sqrt { 89 } }$ m/s