A mass of 100 kg is resting on a rough inclined plane of 60o. If the coefficient of friction is 0.5, then the least force acting parallel to the plane to keep the mass in equilibrium isa)605 Nb)100 Nc)500 Nd)603.7 NCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

The force parallel to the plane but downwards, W = mg.sin 60 = 980 x √3/2 = 848.7N
Maximum friction force acting, f = mg.cos 60 x 0.5 = 980 x ½ x 0.5 = 245N
Thus the minimum extra force required, let say F = 848.7 - 245 = 603.3 N

Answer

HERE, IN Q THERE SHOULD MENTION (g=9.8)....
IF U TAKE g as 10m/s*2 u WILL NOT GET ANSWER.....

Answer

D

Answer

To find the least force acting parallel to the plane to keep the mass in equilibrium, we need to consider the forces acting on the mass on the inclined plane.

1. Weight (W): The weight of the mass is given by the formula W = mg, where m is the mass (100 kg) and g is the acceleration due to gravity (9.8 m/s^2). So, the weight W = 100 kg × 9.8 m/s^2 = 980 N.

2. Normal force (N): The normal force is the force exerted by the inclined plane perpendicular to the surface. It is equal in magnitude and opposite in direction to the component of the weight perpendicular to the plane. The normal force N = mg cosθ, where θ is the angle of inclination (60°). So, N = 100 kg × 9.8 m/s^2 × cos(60°) = 490 N.

3. Frictional force (Ff): The frictional force opposes the motion of the mass on the inclined plane. It is equal to the coefficient of friction (μ) multiplied by the normal force. The coefficient of friction is given as 0.5. So, Ff = μN = 0.5 × 490 N = 245 N.

4. Force parallel to the plane (F): This is the force that needs to be applied parallel to the plane to counteract the frictional force and keep the mass in equilibrium.

To find the value of F, we can use the equation of equilibrium in the horizontal direction:

F - Ff = 0

Substituting the values, we have:

F - 245 N = 0

Solving for F, we get:

F = 245 N

Therefore, the least force acting parallel to the plane to keep the mass in equilibrium is 245 N.

Since none of the provided options match this answer, it appears that there may be an error in the choices given.

Answer

Make FBD of the block, y and x axis perpendicular and along the plane respectively. in y axis, N=mgcos60 .....(1) in x axis, fs +F=mgsin60.....(2) solve then you will get 603.68N

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