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A bullet ofmass m is fired with a veloci...

A bullet ofmass m is fired with a velocity `10m//s` at angle `theta` with horizontal. At the hightest point of its trajectory, it collsides head-on with a bob of mass `3m` suspended by a massless string of length `2//5m` and gets embedded in the bob. After th collision the string moves through an angle of `60^(@)`.
The angle `theta` is

Text Solution

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The correct Answer is:
(i) `37^(@)` (ii) `(120, 45)`
(i) `((u cos theta)/(4))^(2) = 2g ((3R)/(2))`
`rArr cos theta = 4//5 rArr theta = 37^(@)`
(ii) `x = (R )/(2) = (v^(2) sin^(2) theta)/(2g) = 120m`
`y = H = (u^(2) sin^(2) theta)/(2g) = 45m`
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A bullet ofmass m is fired with a velocity 10m//s at angle theta with horizontal. At the hightest point of its trajectory, it collsides head-on with a bob of mass 3m suspended by a massless string of length 2//5m and gets embedded in the bob. After th collision the string moves through an angle of 60^(@) . The horizontal coordinate of the intital position of the bob w.r.t. the point of firing of the bullet is n

A bullet ofmass m is fired with a velocity 10m//s at angle theta with horizontal. At the hightest point of its trajectory, it collsides head-on with a bob of mass 3m suspended by a massless string of length 2//5m and gets embedded in the bob. After th collision the string moves through an angle of 60^(@) . The vertical coordinate of the initial positon of the bob w.r.t. the point of firing of the bullet is

Knowledge Check

  • A bob of mass m, suspended by a string of length l_1 is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l_2 , which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio (l_1)/(l_2) is

    A
    1
    B
    3
    C
    5
    D
    `1//5`

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