Question

A spring of length ‘l’ and force constant k is cut into two pieces of length l/4 and 3l/4. A small block of mass ‘m’ is joined by these spring as shown in such a way that spring are non deformed. Now the block is displaced by a length ‘x’ to the right. The maximum speed attained by the block during its motion assuming that the contact surface is smooth is :

• A.
• B. x
• C. 2x
• D. 4x

Answer 1

Answer: (D)

4x

Answer 2

Using k₁I₁ = k₂I₂ = k$\ell$

$\mathrm { k } _ { 2 } = \frac { \mathrm { k } \cdot \ell } { \ell / 4 } = 4 \mathrm { k }$

Maximum speed is attained when block is passing through the position when springs acquire natural lengths i.e., ∑F_block = 0

Applying W/E theorem

$= \frac { 2 } { 3 } \mathrm { kx } ^ { 2 } + 2 \mathrm { kx } ^ { 2 }$

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