Question

two stones of masses M and 2m are world in horizontal circle the heavy one in radius R by 2 and lighter in radware radius r.the tangential speed of light kee stone is n times they of the value of heavier stone when they experience same centripetal forces . value of n
a.1
b.4
c.2
d.3​

Answer 1

Answer:

The value of n is 2 , the correct answer will be option c

Explanation:

For stone1: mass= M

radius= r

tangential speed of stone1= u

For stone2:  mass = 2m

radius= r /2

tangential speed of stone2= v

Now according t the problem,

u= nv

Now according to the problem the centripetal force of both the stones are same .

Now, According to the formula of centripetal force the value of it for

stone1 = Mu^2/r

for stone 2 = 2mv^2/(r/2)

                  = 4mv^2/r

Now as they are same, then,

Mu^2/r = 4 mv^2/r

or, u^2 = 4v^​2

or, u = 2v

Comparing the values of u  

n = 2

Hence the value of n is 2

Answer 2

Answer:

c. 2

Explanation:

Let the tangential speed of heavier stone be = v

Then, the centripetal force experienced by lighter stone will be -

= (Fc)lighter =m(nv)²r  and

Centripetal force experienced by heavier stone will be -   

= (Fc)heavier=2mv²(r/2)  

Since, (Fc)lighter = (Fc)heavier (Given)  

Therefore,

m(nv)²r=2mv²(r/2)  

n²(mv²r)=4(mv²r)  

n²=4 or

n = 2

Thus, the value of n will be 2.