DOUBTSS:))LOM

\texttt{by pythagoras theorem} \\ \left (\frac{(b-x_1)}{2} \right )^2=d^2+x_2^2\\ \texttt{now u have a constraint binding} \ x_1 \ and \ x_2 \\ \texttt{so u can find} \ \frac{d^2x_2}{dt^2}\texttt{ in terms of } \frac{d^2x_1}{dt^2}\\ \texttt{now write laws of motion equations on both the masses}\\ m_1g-T=m_1\frac{d^2x_1}{dt^2}\\ 2T\cos\theta-m_2g=-m_2\frac{d^2x_2}{dt^2}\\ \texttt{eliminate T and find } \frac{d^2x_1}{dt^2}\\ \texttt{once u get all these u can easily find the P.E and K.E of the individual masses as a function of }x_1\\ \texttt{the system is stable if}\frac{d^2U}{dx_1}(at / x_1 \texttt{in equilibrium point })>0

it doesnt mean that if ur post is not pinked then ur soln is wrong....

Is my soln to ques no.2 wrng??? I thought pink posts sort of confirm if the soln is right or wrong.why didnt i get pinked??(I'M NOT AFTER THE PINK!!)...

@ akhil , i m b4 the pink [3] [3]

for Q 3 i m not sure but i think there isnt much in it

2Tcosθ=m₂g, T=m₁g

so cosθ=m₂2m₁= x₂(b-x₁)/2

and [(b-x₁)/2 ] ² + x₁²=d²
so we can get x₂ in terms of m₁,m₂,b,d

why r u after the PINK????:P

pink ke peeche mat bhaago, pink le dubega !!!

SANCHIT BHAI 3 DOUBT KUCH JAMA NAHI

thnxx dude!!!!!!!!!

2)

After rebound, the body has only horizontal velocity and hence no vertical velocity.
OA=H - h

t₁=√2(H-h)/g

t₂=time to reach from A to B= time to reach from A to B₁=√2h/g

total time from O to B=t₁+t₂
=√2/g(√H-h+√h)

if t depends on h(H and g are constants), then max value of t= dt/dh=0

=d/dh{(H-h)^1/2+h^1/2}=0

or, h/H=1/2 .....(answer)

I WANT A PINK!!!!

2)a body freely falling from a giben height H hits an inclined plane in its path at a height h .as a result of this impact the direction of velocity of the body becomes horizontal .for what values of h/H the body will take maximum time to reach the ground??????

nd wht abt the minimum?????????

3)Consider the system of pulleys, masses, and string shown in the following figure. A light string of length b is attached at point A , passes over a pulley at point B located a distance 2d away, and finally attaches to mass . Another pulley with mass attached passes over the string, pulling it down between A and B . Calculated the distance x₁ when the system is in equilibrium, and determine whether the equilibrium is stable or unstable. The pulleys are massless.....

my 2nd doubt is not yet cleared-post no.5

anyone!!!!

2)a body freely falling from a giben height H hits an inclined plane in its path at a height h .as a result of this impact the direction of velocity of the body becomes horizontal .for what values of h/H the body will take maximum time to reach the ground??????

nd wht abt the minimum?????????

thnxx bhaiiya got my answers were correct