Two blocks with masses 100 g and 200 g are attached to the ends of springs $A$ and $B$ as shown in figure. The energy stored in $A$ is $E$ . The energy stored in $B$ , when spring constants $k_{A}, k_{B}$ of $A$ and $B$ , respectively satisfy the relation $4 k_{A}=3 k_{B^{\prime}}$ , is :

Question

Two blocks with masses 100 g and 200 g are attached to the ends of springs

A

and

B

as shown in figure. The energy stored in

A

is

E

. The energy stored in

B

, when spring constants

k_{A}, k_{B}

of

A

and

B

, respectively satisfy the relation

4 k_{A}=3 k_{B^{\prime}}

, is :

Quantrex Academy · Accepted Answer

Correct answer: C. 3E

For blocks hanging in equilibrium, spring extensions are:

x_A = \frac{m_A g}{k_A} = \frac{100g}{k_A}

and

x_B = \frac{m_B g}{k_B} = \frac{200g}{k_B}

.
Energy stored:

E = \frac{1}{2}k_A x_A^2 = \frac{5000g^2}{k_A}

and

U_B = \frac{1}{2}k_B x_B^2 = \frac{20000g^2}{k_B}

.
Taking ratio:

\frac{U_B}{E} = 4 \cdot \frac{k_A}{k_B}

.
Given

4k_A = 3k_B

, we have

\frac{k_A}{k_B} = \frac{3}{4}

.
Therefore:

U_B = 4E \cdot \frac{3}{4} = 3E

.

Two blocks with masses 100 g and 200 g are attached to the ends of...