A particle is suspended from a string of length R. It is given a velocity u = 3  at the lowest point.           Column I                       Column II    (A) Velocity at B                   (P) 7 mg        (B) Velocity at C                   (Q)         (C) Tension in string at B     (R)        (D) Tension in string at C     (S)    4 mgA-R; B-Q; C-P; D-S    A-Q; B-R; C-S; D-PA-R; B-P; C-Q; D-SA-P; B-S; C-R; D-Q

Three point particles  A,B and C, of masses m,ηm and 2m respectively, are in equilibrium, with the help of strings, as shown:The horizontal level of  A and C is same and the two inclined strings are equal in length. If the ratio of tensions in the two vertical strings is 1.5, findη.

In vertical circular  motion of  a bob, match the entries of list–I with entries of list–II. Here v0 is the velocity of bob at lowest point & T is tension in string.   List-I(speed at lowest point)    List-II(possible situation)(P) v0 =  (1) Tension at lowest point = 6mg(Q)  v0 =  (2) string will slack for a finite time(R) v0 = 2 (3) bob will oscillate(S) v0 = 3 (4) Tension at highest point = 4mg        P    Q   R   S(A)    1    2    3    4(B)    4    2    3    1(C)    1    3    2    4(D)    4    3    2    1ABCD

(c) the tension of the string when the bob is at point B.

A particle moves along a straight line such that its displacement at any time t is given by S = t3 – 6t2 + 3t + 4 metres. The velocity when the acceleration is zero is :4 ms–1– 12 ms–1 42 ms–1– 9 ms–1

A particle P is moving along a straight line through the fixed point O.The displacement, s metres, of P from O at time t seconds is given bys = t 3 – 27t + 55 t . 0(a) Write down the distance, in metres, of P from O when t = 0(1)(b) Find an expression, in terms of t, for the velocity, v m/s, of P at time t seconds.(2)(c) Find the value of t when P is closest to O.(2)(d) Find the distance, in metres, of P from O when P is closest to O.(1)(e) Find the distance, in metres, travelled by P in the interval 0 - t - 5(3)..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................