Answer to Question #132158 in Mechanics | Relativity for viccy

Question

a block of mass m is kept over a fixed wedge inclined at 30 degree angle .block is attached to a shere of same mass as shown in figure.sphere is dipped in water.find the acceleration of sphere.

Answer 1

Explanations & Calculations

• Consider the figure above to get an understanding of the sum.
• When the system is released from the rest, sphere drags the whole system downwards as the weight force along that direction is greater.
• As it's dipped in water an upthrust force acts a shown which reduces the acceleration of the system compared to when the sphere is in air.

• Apply Newtons second law on the two masses to find the acceleration.

$\qquad\qquad \begin{aligned} \small mg-U-T &= \small ma\cdots\cdots(1; \text{for the sphere}) \\ \small T-mg\sin30 &= \small ma\cdots\cdots({2; \text{foor the }block})\\ \small mg-U-\frac{mg}{2} &= \small 2ma \cdots(1+2)\\ \small \frac{mg}{2}-U &= \small 2ma\\ \small \frac{mg}{2}-V\rho g &= \small 2ma\\ \small \frac{mg}{2}-\frac{m}{d}\rho g &= \small 2ma\\ \small \frac{g}{2}\Big(\frac{1}{2} -\frac{\rho}{d} \Big) &= \small a\\ \small \bold{a} &= \small \bold{\small \frac{g}{4}\Big(1 -\frac{2\rho}{d} \Big)} \end{aligned} \\$