The original length of a spring is 25 cm. It elongates 2 cm if a force of 0.96 N is exerted on it. A container is filled with water and one end of the spring is fixed 30 cm above the surface of the water in the container. A wooden block of mass 32 g and of density 0.4 g / cm 3 is hanged onto the other end of the spring. The height of the block is 5 cm. To what depth (in mm) does the block sink into the water? [Take g =10 ms -2 ]

Question

The original length of a spring is 25 cm. It elongates 2 cm if a force of 0.96 N is exerted on it. A container is filled with water and one end of the spring is fixed 30 cm above the surface of the water in the container. A wooden block of mass 32 g and of density 0.4 g / cm 3 is hanged onto the other end of the spring. The height of the block is 5 cm. To what depth (in mm) does the block sink into the water? [Take g =10 ms -2 ] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/ba921a44552bc67e5b941c4394edd71c-.png" /> 30-(25+ x 0)=5- x 0 V =(32/0.4)=80 cc A =16 cm 2 kx 0+103 × 16 × 10-4 × x 0 × 10 =32 × 10-3 × 10 x 0(48+16)=32 × 10-2 x 0=(32/64) cm =5 mm

30−(25+x0​)=5−x0​ V=0.432​=80cc A=16cm2 kx0​+103×16×10−4×x0​×10 =32×10−3×10 x0​(48+16)=32×10−2 x0​=6432​cm=5mm

$30 - (25 + x_{0}) = 5 - x_{0}$
$V = \frac{32}{0.4} = 80 cc$
$A = 16 c m^{2}$
$k x_{0} + 1 0^{3} \times 16 \times 1 0^{- 4} \times x_{0} \times 10$
$= 32 \times 1 0^{- 3} \times 10$
$x_{0} (48 + 16) = 32 \times 1 0^{- 2}$
$x_{0} = \frac{32}{64} c m = 5 mm$