Question

If a particle is in equilibrium under the action of three forces, then show that ratio of each force and sine of angle between the other two forces is constant?

Solution

Let the three forces $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ acting at point O be in equilibrium.

Taking cross product of C on both sides, we get
$open parentheses straight A with rightwards harpoon with barb upwards on top space plus space straight B with rightwards harpoon with barb upwards on top space plus space straight C with rightwards harpoon with barb upwards on top close parentheses cross times straight C with rightwards harpoon with barb upwards on top space equals space 0 space cross times space straight C with rightwards harpoon with barb upwards on top space equals space 0 space rightwards double arrow space straight A with rightwards harpoon with barb upwards on top space cross times space straight C with rightwards harpoon with barb upwards on top space plus space straight B with rightwards harpoon with barb upwards on top space cross times space straight C with rightwards harpoon with barb upwards on top space plus straight C with rightwards harpoon with barb upwards on top cross times straight C with rightwards harpoon with barb upwards on top space equals space 0 space rightwards double arrow space minus space space straight C with rightwards harpoon with barb upwards on top space cross times straight A with rightwards harpoon with barb upwards on top space plus space straight B with rightwards harpoon with barb upwards on top space cross times space straight C with rightwards harpoon with barb upwards on top space plus space 0 space equals space 0 space rightwards double arrow space straight C with rightwards harpoon with barb upwards on top space cross times straight A with rightwards harpoon with barb upwards on top space equals space space straight B with rightwards harpoon with barb upwards on top space cross times space straight C with rightwards harpoon with barb upwards on top rightwards double arrow space fraction numerator straight A over denominator sin space straight alpha end fraction space equals space fraction numerator straight B over denominator space sin space straight beta end fraction space space space space space space space space space space space space space space space space... space left parenthesis 2 right parenthesis space Now comma space taking space the space cross space product space of space equation space left parenthesis 1 right parenthesis space with space straight B with rightwards harpoon with barb upwards on top comma space we space have space space space space open parentheses straight A with rightwards harpoon with barb upwards on top space plus space straight B with rightwards harpoon with barb upwards on top space plus space straight C with rightwards harpoon with barb upwards on top close parentheses space cross times space straight B with rightwards harpoon with barb upwards on top space equals space 0 space cross times space straight B with rightwards harpoon with barb upwards on top space equals space 0 rightwards double arrow straight A with rightwards harpoon with barb upwards on top space cross times straight B with rightwards harpoon with barb upwards on top space plus space space straight B with rightwards harpoon with barb upwards on top space cross times space straight B with rightwards harpoon with barb upwards on top space plus straight C with rightwards harpoon with barb upwards on top space cross times straight B with rightwards harpoon with barb upwards on top space space equals space 0 space rightwards double arrow space straight A with rightwards harpoon with barb upwards on top space cross times straight B with rightwards harpoon with barb upwards on top space plus 0 space minus space straight B with rightwards harpoon with barb upwards on top space cross times space straight C with rightwards harpoon with barb upwards on top space equals space 0 rightwards double arrow space straight A with rightwards harpoon with barb upwards on top space cross times straight B with rightwards harpoon with barb upwards on top space equals space space straight B with rightwards harpoon with barb upwards on top space cross times space straight C with rightwards harpoon with barb upwards on top rightwards double arrow space space space AB space sin space straight gamma space equals space BC space sin space straight alpha space rightwards double arrow space fraction numerator straight A over denominator sin space straight alpha space end fraction space equals space fraction numerator straight C over denominator sin space straight gamma end fraction space space space space space space space space space space space space space space space space space space space space space space... space left parenthesis 3 right parenthesis thin space From space equation space left parenthesis 2 right parenthesis space and space left parenthesis 3 right parenthesis comma space we space get fraction numerator straight A over denominator sin space straight alpha space end fraction space equals space fraction numerator straight B over denominator sin space straight beta end fraction space equals space fraction numerator straight C over denominator sin space straight gamma end fraction space space space space space$

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Motion In A Plane

If a particle is in equilibrium under the action of three forces, then show that ratio of each force and sine of angle between the other two forces is constant?

Some More Questions From Motion in A Plane Chapter

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Motion In A Plane

If a particle is in equilibrium under the action of three forces, then show that ratio of each force and sine of angle between the other two forces is constant?

Some More Questions From Motion in A Plane Chapter

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.