question_answer

Which of the following exerts greater thrust? (a) A spherical object of radius 7 cm and density \[0.21\text{ }g\text{ }c{{m}^{-3}}\]placed on a table (b) A cylindrical object of length 49 cm, radius 7 cm and density \[2.2\text{ }g\text{ }c{{m}^{-3}}\]placed on a table (Acceleration due to gravity is \[9.8\text{ }m{{s}^{-2}}\])

Answer:

(a) Radius of the sphere\[(r)=7\text{ }cm\] Density of the sphere\[(d)=0.21\text{ }g\text{ }c{{m}^{3}}\] Thrust \[(T)=mg\] Let us first calculate the mass of the sphere. \[Mass=volume\times density\] \[=\frac{4}{3}\pi {{r}^{3}}\times d=\frac{4}{3}\pi {{(7)}^{3}}\times 0.21\] \[Mass=\frac{4}{3}\pi \times 343\times 0.21=30.184\,kg\] \[Mass=301.84\times \frac{1}{1000}\times kg=0.30184\,kg\] Thrust \[=0.30184\times 10\text{ }N\] Therefore, force exerted by the sphere is 3.0184 N (b) Radius of the base \[(r)=7\text{ }cm\] Length of the cylinder \[(l)=49\text{ }cm\] Density \[(d)=2.2\text{ }g\text{ }c{{m}^{3}}\] Acceleration due to gravity\[(g)=10\text{ }m{{s}^{2}}\] To find the thrust exerted, first we have to calculate the mass of the cylinder. Mass of the cylinder \[=V\times d\] \[=\pi {{r}^{3}}\ell \times d\](\[\because \]volume of the cylinder\[=p{{r}^{2}}l\]) \[=\frac{22}{7}\times 7\times 7\times 49\times 2.2=16601.2g\] \[=16601.2\times \frac{1}{1000}kg=16.601\,\,kg\]                                 \[\because \]Thrust exerted \[=mg\] \[=16.601\times 10=166.01\text{ }N.\] So, the thrust exerted by the cylinder is greater than the sphere.