In the adjacent figure, the cross section ABCD of a vertical square column is shown as seen from top. One end of a light inextensible and inelastic string of length 4√2 m is attached to the point A of column and wrapped tightly in a clockwise sense. A small bob S is connected to the other end of the string. Keeping the string taut, the bob S is given a horizontal speed V₀ = 3.5 m/s at an angle 45° with the side AD near the point A. Calculate the time (to the nearest integer) taken by the string to get unwrapped (up to the instant when string just loses contact with AB part).
Physics · Mixed Chapter
JEE Mains

Question

In the adjacent figure, the cross section ABCD of a vertical square column is shown as seen from top. One end of a light inextensible and inelastic string of length 4√2 m is attached to the point A of column and wrapped tightly in a clockwise sense. A small bob S is connected to the other end of the string. Keeping the string taut, the bob S is given a horizontal speed V₀ = 3.5 m/s at an angle 45° with the side AD near the point A. Calculate the time (to the nearest integer) taken by the string to get unwrapped (up to the instant when string just loses contact with AB part).

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The bob travels along a succession of circular arcs about the successive corners of the square as the string unwraps. The tension is perpendicular to the instantaneous velocity, so the bob’s speed remains V₀=3.5 m s⁻¹. Step 2: For each segment of the unwinding motion, use arc length sᵢ=rᵢΔθᵢ, with the radius equal to the remaining free string length. Step 3: Add the arc lengths until the segment AB is fully released and divide the total by 3.5 m s⁻¹; round the time to the nearest whole…