Question

A mass M is suspended by two springs of force constants K­₁ and K₂ respectively as shown in the diagram. The total elongation (stretch) of the two springs is

• A. $\frac { M g } { K _ { 1 } + K _ { 2 } }$
• B. $\frac { M g \left( K _ { 1 } + K _ { 2 } \right) } { K _ { 1 } K _ { 2 } }$
• C. $\frac { M g K _ { 1 } K _ { 2 } } { K _ { 1 } + K _ { 2 } }$
• D. $\frac { K _ { 1 } + K _ { 2 } } { K _ { 1 } K _ { 2 } M g }$

Answer 1

Answer: (B)

$\frac { M g \left( K _ { 1 } + K _ { 2 } \right) } { K _ { 1 } K _ { 2 } }$

Answer 2

For series combination

$k _ { e q } = \frac { k _ { 1 } k _ { 2 } } { k _ { 1 } + k _ { 2 } }$

$\Rightarrow x = \frac { m g \left( k _ { 1 } + k _ { 2 } \right) } { k _ { 1 } k _ { 2 } }$