Question

1)A uniform wire of length 1 m and radius 0.028 cm is employed to raise a stone of
density 2500 kg/m3 immersed in water. Find the change in the elongation of wire when
the stone is raised out of water.
[ mass of stone = 5 kg, Y of material of wire = 2 x 1011 N/m2,]

2)Find the maximum velocity and maximum acceleration of a particle performing S.H.M.
whose displacement is x = 2cos (50t) cm.

3)A light spring is stretched by 50 g force through a distance of 10 cm. A mass of 100 g
is attached to the spring and set into oscillations. Find the periodic time of its oscillation
and spring constant.

Answer 1

1)

$$Y=\frac{FL}{A\Delta L}=\frac{(1-\frac{\rho_w}{\rho})mgL}{\pi r^2\Delta L}$$

$$2\cdot 10^{11}=\frac{(1-\frac{1000}{2500})(5)(9.8)(1)}{\pi ( 0.00028)^2\Delta L}$$

$$\Delta L=0.0006\ m=0.6\ mm$$

2)

$$V=\omega A=(50)(2)=100\frac{cm}{s}=1\frac{m}{s}$$

$$a=\omega^2 A=(50)^2(2)=5000\frac{cm}{s^2}=50\frac{m}{s^2}$$

3)

$$kx=mg$$

$$0.1k=(0.05)(10)$$

The spring constant:

$$k=5\frac{N}{m}$$

The period:

$$T=2\pi\sqrt{\frac{m}{k}}$$

$$T=2\pi\sqrt{\frac{0.1}{5}}=0.89\ s$$