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A block with a square base measuring axx...

A block with a square base measuring `axxa` and height h, is placed on an inclined plane. The coefficient of friction is `mu`. The angle of inclination `(theta)` of the plane is gradually increased. The block will

A

topple before sliding if `mu gt (a)/(h)`

B

topple before sliding if `mu lt (a)/(h)`

C

slide before toppling if `mugt(a)/(h)`

D

slide before toppling if `mugt(a)/(h)`

Text Solution

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The correct Answer is:
A, D
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A block of mass m is placed on a rough inclined plane. The corfficient of friction between the block and the plane is mu and the inclination of the plane is theta .Initially theta=0 and the block will remain stationary on the plane. Now the inclination theta is gradually increased . The block presses theinclined plane with a force mgcostheta . So welding strength between the block and inclined is mumgcostheta , and the pulling forces is mgsintheta . As soon as the pulling force is greater than the welding strength, the welding breaks and the blocks starts sliding, the angle theta for which the block start sliding is called angle of repose (lamda) . During the contact, two contact forces are acting between the block and the inclined plane. The pressing reaction (Normal reaction) and the shear reaction (frictional force). The net contact force will be resultant of both. Answer the following questions based on above comprehension: Q. If mu=(3)/(4) then what will be frictional force (shear force) acting between the block and inclined plane when theta=30^@ :

A block of mass m is placed on a rough inclined plane. The corfficient of friction between the block and the plane is mu and the inclination of the plane is theta .Initially theta=0 and the block will remain stationary on the plane. Now the inclination theta is gradually increased . The block presses theinclined plane with a force mgcostheta . So welding strength between the block and inclined is mumgcostheta , and the pulling forces is mgsintheta . As soon as the pulling force is greater than the welding strength, the welding breaks and the blocks starts sliding, the angle theta for which the block start sliding is called angle of repose (lamda) . During the contact, two contact forces are acting between the block and the inclined plane. The pressing reaction (Normal reaction) and the shear reaction (frictional force). The net contact force will be resultant of both. Answer the following questions based on above comprehension: Q. For what value of theta will the block slide on the inclined plane:

A block of mass m is placed on a rough inclined plane. The corfficient of friction between the block and the plane is mu and the inclination of the plane is theta .Initially theta=0 and the block will remain stationary on the plane. Now the inclination theta is gradually increased . The block presses theinclined plane with a force mgcostheta . So welding strength between the block and inclined is mumgcostheta , and the pulling forces is mgsintheta . As soon as the pulling force is greater than the welding strength, the welding breaks and the blocks starts sliding, the angle theta for which the block start sliding is called angle of repose (lamda) . During the contact, two contact forces are acting between the block and the inclined plane. The pressing reaction (Normal reaction) and the shear reaction (frictional force). The net contact force will be resultant of both. Answer the following questions based on above comprehension: Q. If the entire system, were accelerated upward with acceleration a the angle of repose, would:

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