Can someone help me to solve this question please! with an explanation thanks Di

Question

Can someone help me to solve this question please! with an explanation thanks

Dinosaurs dominated life on Earth for millions of years and then disappeared very suddenly. In the experimentation and data-collecting stage, paleontologists studied fossils and skeletons found in rocks in various layers of Earth's crust. Their findings enabled them to map out which species existed on Earth during specific geologic periods. They also revealed no dinosaur skeletons in rocks formed immediately after the Cretaceous period which dates back some million year 65 It is therefore assumed that the dinosaurs became extinct about 65 million years ago. Among the many hypotheses put forward to account for their disappearance were disruptions of the food chain and a dramatic change in climate caused by violent volcanic eruptions. However, there was no convincing evidence for any one hypothesis until 1977. It was then that a group of paleontologists working in Italy obtained some very puzzling data at a site near Gubbio. The chemical analysis of a layer of clay deposited above sediments formed during the cretaceous period (and therefore a layer that record events occurring after the cretaceous period) showed a surprisingly high content of the element iridium. Iridium is very rare in Earth's crust but is comparatively abundant in asteroids. This investigation led to the hypothesis that the extinction of dinosaurs occurred as follows. To account for the quantity of iridium found, scientists suggested that a large asteroid several miles in diameter hit Earth about the same time the dinosaurs disappeared. The impact of the asteroid on Earth's surface must have been so tremendous that it literally vaporized a large quantity of surrounding rocks, soils, and other objects The resulting dust and debris floated through the air and blocked the sunlight for months or perhaps years. Without ample sunlight, most plants could not grow, and the fossil of record confirms that many types of plants did indeed die out at this time. Consequently, course, many plant-eating animals gradually perished, and then, in turn, meat-eating animals began to starve. Limitation of food sources obviously affects large animals needing great amounts of food more quickly and more severely than small animals. Therefore, the huge dinosaurs vanished due to lack of food and Available evidence suggests that about 20% of the asteroid's mass turned to dust spread uniformly over Earth after eventually settling out of the upper atmosphere. This dust amounted to about 0.02 g/cm^2 of Earth's surface. The asteroid very likely had a density of about 2 g/cm^3. Calculate the mass (in kg) of the asteroid and its radius in meters assuming that it was a perfect sphere. (The area of Earth is 5.1 times 10^14 m^2 Compare the radius of this asteroid to the radius of the Chelabinsk meteor, which dramatically entered Earth's atmosphere on February 15, 2013

Explanation / Answer

dust = 0.02 g/cm2 of earths surface

1cm2 of earth's surface occupies 0.02 gm

1cm= 0.01 m

(0.01)2 m2 of earth's surface occupies 0.02 gm

0.001 m2 occupies 0.02 gm of dust

5.1*1014m2 of eath correspond to 5.1*1014*0.001 gm of dust= 5.1*1010 gm of dust =5.1*1010/103 kg of dust =5.1*107 kg of dust

This correspond to 20% of mass of asteroid's mass =5.1*107/0.2 =2.55*108 kgs

density of asetoid =2 g/cc =2000 kg/m3

Volume = mass/density = 2.55*108/2000 =127500 m3

Volume of sphere = (4/3)*Pi*r3, where r is the radius of the sphere

hence 4.19r3= 127500

r =31.22 m, diamter =3*31.22= 62.44 m

diamter of chelabinsk = 20 m

almost =(20/62.44)*100=32.03% of diameter of asteriid

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