Q.A particle of mass 1 kg, tied to a 1.2 m long string is whirled to perform vertical circular motion, under gravity. Minimum speed of the particle (at the uppermost point of its path) is 5 m/s. Consider the following statements. P) Maximum speed (at the lowermost point) must be $5\sqrt{5}$ m/s.
Q) Difference between the maximum and minimum tensions along the string is 60 N. Select the correct option. (A) Only the statement P is correct.
(B) Only the statement Q is correct.
(C) Both the statements are correct.
(D) Both the statements are incorrect.

The tension difference $T_B-T_A=6mg=60$ N is a fixed result (Eq. 1.15), independent of v and r, so statement Q is always true; but computing $v_B$ from the given string length (r = 1.2 m) and $v_A=5$ m/s gives $v_B=\sqrt{73}\approx8.54$ m/s, not $5\sqrt5\approx11.18$ m/s, so P is false.

This is a vertical circular motion under gravity with a string of length (and hence radius) r = 1.2 m, mass m = 1 kg, minimum (uppermost) speed $v_A=5$ m/s (use g = 10 m/s^2). Checking statement Q first, since it uses the most general result: subtracting the force equations at the top ($mg+T_A=mv_A^2/r$) and bottom ($T_B-mg=mv_B^2/r$) and using energy conservation ($v_B^2-v_A^2=4gr$) between them always gives $T_B-T_A=6mg$ -- notice r and the speeds cancel out completely in this derivation, so this holds for ANY valid vertical circular motion, not just the borderline minimum-energy case. Here $T_B-T_A=6(1)(10)=60$ N, exactly matching statement Q, so Q is TRUE. Now checking statement P: using energy conservation with the ACTUAL radius r = 1.2 m and $v_A=5$ m/s, $v_B^2=v_A^2+4gr=25+4(10)(1.2)=25+48=73$, so $v_B=\sqrt{73}\approx8.54$ m/s. Statement P claims $v_B=5\sqrt5=\sqrt{125}\approx11.18$ m/s, which does not match -- P would only be true if $v_A$ happened to equal the CRITICAL minimum $\sqrt{rg}=\sqrt{12}\approx3.46$ m/s for this particular r, but the given $v_A=5$ m/s is larger than that critical value (which is perfectly consistent physically -- the string can carry more tension than the bare minimum), so P's specific numeric claim does not follow.

Use the general, speed-and-radius-independent result $T_B-T_A=6mg$ (from subtracting the top/bottom force equations and using energy conservation) to check Q directly, and use energy conservation with the given r and $v_A$ to compute the actual $v_B$ for checking P.

Assuming the given 'minimum speed' $v_A=5$ m/s must equal the critical borderline value $\sqrt{rg}$ for the given radius, when in fact it is simply the ACTUAL speed at the top (which can be, and here is, larger than the bare minimum needed to keep the string taut).