A given object takes n times as much time to slide down a 45° rough incline as it takes to slide down a perfectly smooth 45° incline. The coefficient of kinetic friction between the object and the incline is given by

(1) $\left(1-\frac{1}{n^2}\right)$

(2) $\frac{1}{1-n^2}$

(3) $\sqrt{\left(1-\frac{1}{n^2}\right)}$

(4) $\sqrt{\frac{1}{1-n^2}}$

Starting from rest, a body slides down a 45° inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is 

(1) 0.33

(2) 0.25

(3) 0.75

(4) 0.80

A force of 750 N is applied to a block of mass 102 kg to prevent it from sliding on a plane with an inclination angle 30° with the horizontal. If the coefficients of static friction and kinetic friction between the block and the plane are 0.4 and 0.3 respectively, then the frictional force acting on the block is 

(1) 750 N

(2) 500 N

(3) 345 N

(4) 250 N

A body takes time t to reach the bottom of an inclined plane of angle θ with the horizontal. If the plane is made rough, time taken now is 2t. The coefficient of friction of the rough surface is

(1) $\frac{3}{4}\tan \theta$

(2) $\frac{2}{3}\tan \theta$

(3) $\frac{1}{4}\tan \theta$

(4) $\frac{1}{2}\tan \theta$

A block is kept on an inclined plane of inclination θ of length l. The velocity of particle at the bottom of inclined is (the coefficient of friction is μ)

(1) $\sqrt{2gl(\mu \cos \theta -\sin \theta )}$

(2) $\sqrt{2gl(\sin \theta -\mu \cos \theta )}$

(3) $\sqrt{2gl(\sin \theta +\mu \cos \theta )}$

(4) $\sqrt{2gl(\cos \theta +\mu \sin \theta )}$

A block of mass \(m\) lying on a rough horizontal plane is acted upon by a horizontal force \(P\) and another force \(Q\) inclined at an angle \(\theta\) to the vertical. The block will remain in equilibrium if the coefficient of friction between it and the surface is: 

                        
1. \(\frac{(P+Q\sin\theta)}{(mg+Q\cos\theta)}\)

2. \(\frac{(P\cos\theta+Q)}{(mg-Q\sin\theta)}\)

3. \(\frac{(P+Q\cos\theta)}{(mg+Q\sin\theta)}\)

4. \(\frac{(P\sin\theta-Q)}{(mg-Q\cos\theta)}\)

A block of mass 0.1 kg is held against a wall by applying a horizontal force of 5 N on the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of the frictional force acting on the block is 

(1) 2.5 N

(2) 0.98 N

(3) 4.9 N

(4) 0.49 N

What is the maximum value of the force \(F\) such that the block shown in the arrangement, does not move?

 
1. \(20~\)N
2. \(10~\)N
3. \(12~\)N
4. \(15~\)N

A body of mass m rests on horizontal surface. The coefficient of friction between the body and the surface is μ. If the mass is pulled by a force P as shown in the figure, the limiting friction between body and surface will be 

(1) μmg

(2) $\mu \left[mg+\left(\frac{{\displaystyle P}}{{\displaystyle 2}}\right)\right]$

(3) $\mu \left[mg-\left(\frac{{\displaystyle P}}{{\displaystyle 2}}\right)\right]$

(4) $\mu \left[mg-\left(\frac{{\displaystyle \sqrt{3}P}}{{\displaystyle 2}}\right)\right]$

A 40 kg slab rests on a frictionless floor as shown in the figure. A 10 kg block rests on the top of the slab. The static coefficient of friction between the block and slab is 0.60 while the kinetic friction is 0.40. The 10 kg block is acted upon by a horizontal force 100 N. If g = 9.8 m/s², the resulting acceleration of the slab will be 

(1) 0.98 m/s²

(2) 1.47 m/s²

(3) 1.52 m/s²

(4) 6.1 m/s²