A stone of mass 10 kg is placed on the horizontal floor and it is pulled by a force F acting at angle 45°. What is tension in the string when it breaks off from the ground? (g = 10m/s2).

The stone will just lose the contact when vertical component of applied force i.e. F sin45° is equal to the weight of stone i.e. 100N


The stone will just lose the contact when vertical component of appli
Therefore tension in string is 100 square root of 2 straight N.
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Two particles A and B start from P and move along a circular path in anticlockwise and clockwise direction respectively. They complete one fourth of the journey in same time. Do they have same average velocities?
               

The particles undergo different displacement. So, the two particles do not have the same average velocity. 

Here, the magnitude of displacement, that is, the distance travelled by the two partcles is same. Therefore, they may have the same speed. 
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A girl walks 100 m at angle of 30° North of West. What is the ratio of the distance travelled by the girl in North to West direction?


Total distance covered by the girl is equal to total displacement = 100m

Angle,  = 30o

Magnitude of the component of displacement along North is, 


Magnitude of the component of displacement along West is,

Therefore, the ratio of the distance travelled by the girl in North to West direction is given by, 

  
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The position of particle at any instant is given by straight r with rightwards arrow on top equals 50 straight t straight j with hat on top plus 5 straight t squared straight i with hat on topAt what instant the velocity vector will make an angle 45° with X-axis?

Given,

Position of the particle, 

∴ Velocity,  

                 

The angle which the velocity vector makes with X-axis at any instant is,

 

Here, 

Therefore,

        

          

So, when time is 5 seconds, the velocity vector will make an angle 450 with x-axis. 

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The position of a particle is given by
                space straight r with rightwards arrow on top equals 3 straight t straight i with hat on top minus 2 straight t squared straight j with hat on top plus 4 straight k with hat on top
where t is in second and r is in meter.
(a) Find the straight v with rightwards arrow on top space and space straight a with rightwards arrow on top of the particle.
(b) What is the magnitude and direction of velocity of the particle at t = 2s?


(a)

Given,

Position of the particle,



Velocity,



and,

Acceleration,
                        

(b) Now,

Velocity,

At time = 2 sec, 

           

∴  

and

At t = 2 sec,

Acceleration, 

∴         and directed towards negative direction of X-axis. 

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