A block of mass is (1) pushed in case (A) and (2) pulled in case (B) , by force , making an angle of with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is . The difference between the accelerations of the block, in case (B) and case (A) will be:

A block of mass is (1) pushed in case (A) and (2) pulled in case (B) , by force , making an angle of with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is . The difference between the accelerations of the block, in case (B) and case (A) will be:

1. A
2. B
3. C
4. D

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Solution:

Concept- Frictional force is the product of friction coefficient and normal force. We are applying force to the horizontal surface in two ways and at an angle. To find the vertically and horizontally acting forces on the blocks, we must divide this force into vertical and horizontal components. This allows us to calculate the acceleration of the blocks.
Used formula:
, where is the mass and is the acceleration.
, where is the frictional force, is the coefficient of friction and is the normal force.
First, we can consider the case A. We are trying to push the block of mass with a force . But we are pushing the block with an angle to the horizontal. We can split this force into two so that we can find the normal force. The force can be split into and . Here the force is and the angle is . Thus,
Normal force, Weight and vertical components of force are both acting in the same direction in this case. As a result, they will be added up.
Here We can calculate the frictional force (f) by multiplying the normal force by the coefficient of friction between the block and the floor.  To determine the actual force on the block, subtract the frictional force from the horizontal force. As a result, the block's pushing force in the direction of motion is,
The block's acceleration will be equal to the ratio of its actual force to its mass.
The second case B will be considered next. We are pulling the block at a 30 degree angle to the horizontal. To find the normal force and force along the horizontal line, we must divide the force.
Normal force, In this case, the weight is acting in the opposite direction of the vertical component of the force we applied. That's why we're using a minus sign instead of a plus sign here.
To calculate the frictional force, multiply it by the normal force acting on the block.
To obtain the actual force, this frictional force must be subtracted from the force acting on the horizontal line. Thus,
The acceleration of this block can be calculated by dividing the actual force on the block by its mass.So the change in acceleration will be equal to,
Hence, option 2 is the correct answer.

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