How to Find Acceleration Due to Gravity at Different Heights?

By Team Aakash Byju's | 10th November 2022 Chat Box

What is the value of acceleration due to gravity at a height equal to half the radius of the earth from the surface of the earth? [Assume g = 10 ms at earth's surface]

[{"selector":"#anim-6f08be6b-290d-4b39-9611-5ad27c6c90ae","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-a41fc3e9-64d8-48f3-aed1-07fc4d726bea","keyframes":{"transform":["translate3d(-991.305%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-4fd2e387-b460-4639-bcfd-e58ba2536d0c","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-75292d8e-687c-4f16-8acf-d302aee43406","keyframes":{"transform":["translate3d(-116.49485%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] -2

The acceleration due to gravity at a height equal to half the radius of the earth from the surface of the earth is 40 ms.

[{"selector":"#anim-d4ceea2a-dbee-4246-816d-78ef9af19f17","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-c4f90e8a-13e7-4f8b-9ac3-92399a84494c","keyframes":{"transform":["translate3d(-116.49485%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-af4a5293-8224-4b92-954b-62de412a733e","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-b2e681e1-c6a1-4362-9f38-e13784a350d4","keyframes":{"transform":["translate3d(-1365.2184%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] -2

The expression for the acceleration on the surface of the earth due to gravity is

[{"selector":"#anim-96ce463f-e4ad-4093-b1ec-87a6822cd331","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-64be4872-f091-4ac0-a377-c414953e747e","keyframes":{"transform":["translate3d(-116.49485%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-8ea92394-121f-4f70-ad11-79e3bb4032dd","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-b230aa4e-cb16-4ffd-a6c7-832940446bdb","keyframes":{"transform":["translate3d(-115.55555%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] GM R 2 g = Where, G is the gravitational constant M is the mass of the earth and R is the radius of the earth.

The acceleration at any height due to gravity is

[{"selector":"#anim-a7122b3b-74ef-4713-a5ab-13d0f19a577a","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-93a24a7c-7dfe-443e-847f-2732346731ad","keyframes":{"transform":["translate3d(-116.49485%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] a = GM h 2

To find the acceleration due to gravity at a height equal to half the radius of the earth, we need to write

[{"selector":"#anim-3eefadbd-9fab-4256-bf0e-da8416cbf320","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-d8046eff-01e2-497e-8593-0dcb0e72d260","keyframes":{"transform":["translate3d(-116.49485%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] R 2 a GM R 2 2 = GM R 2 4 = 4 GM R 2 h = = =

But, we know that

[{"selector":"#anim-66e81252-bab4-46bb-b108-7307ea2da629","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-b28e0686-52d1-485b-9159-42ea202386e1","keyframes":{"transform":["translate3d(-116.49485%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-a4201f1b-08fc-4c1d-9d9e-22a0f1c62b55","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-8d440cac-6bf1-4c0f-a7c8-898560237684","keyframes":{"transform":["translate3d(-119.83805%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-8e01cc58-33aa-4f7c-a25d-ea0746ea7dfd","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-b8fab49d-0b13-472a-b684-cc22307e724b","keyframes":{"transform":["translate3d(-1404.99962%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-4b373474-ecf9-49da-94af-2dfda1ed77f5","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-35fa52fc-cbde-469d-9c35-4cb4e848eb82","keyframes":{"transform":["translate3d(-121.12068%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-807f61b8-1aec-454b-9432-645b7b5952ca","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-31c6bd36-1e08-4fe5-815e-220601e1be25","keyframes":{"transform":["translate3d(-1239.99984%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-81d0de95-03ff-4f7f-b059-f997fba8f4c9","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-a0e245d6-6b00-46fc-a546-8f74e719e801","keyframes":{"transform":["translate3d(-134.16668%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] g = GM R 2 Thus a = 4g It is given that g = 10 ms. -2 so a = 4 × 10 = 40ms. -2

Read More Stories

[{"selector":"#anim-3ffa3035-7567-4d98-b8fc-dd64e09f9a1b","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-2aba656f-1df5-4fca-adb4-68f85ddf4e56","keyframes":{"transform":["translate3d(-142.37287%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-71bfa49e-304a-4f9b-90d7-0d66e7830f78","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-adf8dcc5-cae8-4525-ace0-b6ef989184a1","keyframes":{"transform":["translate3d(-143.22033%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-2060fce6-615a-453c-b3d3-bc4e87b5fec5","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-98eb193e-29de-419f-bcb2-6b6c40031485","keyframes":{"transform":["translate3d(125.82416%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-3acb5656-b620-4586-98a0-6a92a728cee3","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-3b1504a2-6c63-4355-afd6-0b00dde17bf7","keyframes":{"transform":["translate3d(126.37361%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] Explained: What is Lens Maker Formula? Why Is It Called So? Relationship Between Angle of Incidence, Angle of Prism and Minimum Deviation Download Aakash App