Question

If we throw a body upwards with velocity of at what height its kinetic energy reduces to half of the initial value ? Take $g = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$

• A. 4m
• B. 2 m
• C. 1 m
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

We know kinetic energy $K = \frac { 1 } { 2 } m v ^ { 2 }$ ∴ $v \propto \sqrt { K }$

When kinetic energy of the body reduces to half its velocity becomes v = $\frac { u } { \sqrt { 2 } } = \frac { 4 } { \sqrt { 2 } } = 2 \sqrt { 2 } \mathrm {~m} / \mathrm { s }$

From the equation $v ^ { 2 } = u ^ { 2 } - 2 g h$

⇒ $( 2 \sqrt { 2 } ) ^ { 2 } = ( 4 ) ^ { 2 } - 2 \times 10 h$ ∴ $h = \frac { 16 - 8 } { 20 } = 0.4 m$ .