Two boys are standing at the ends A and B of a ground, where AB= a. The boy at B starts running in a direction perpendicular to AB with velocity The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is
A force F is given F = at + bt2 where, t is time. What are the dimensions of a and b?
[ M L T-1 ] and [M L To ]
[ M L T-3 ] and [ M L2 T-4 ]
[ M L T-4 ] and [ M L T1 ]
[ M L T-3 ] and [ M L T-4 ]
A particle moves towards east for 2 s with velocity 15 m/s and move towards north for 8 s with velocity 5 m/s. Then, average velocity of the particle is
1 m/s
5 m/s
7 m/s
10 m/s
The distance x (in µm) covered by a molecule starting from point A at time t = 0 and stopping at another point B in given by the equation The distance between A and B ( in μm) is closed to
10.7
20.7
40.7
50.7
The density of a rod having length l varies as ρ = c + dx, where x is the distance from the left end. The centre of mass is
A.
Let the cross-sectional area is . The mass of an element of length dx located at a distance x away from the left end is (C + Dx) dx. The x-coordinate of the centre of mass is given by
=
Where limit is from 0 to l.
=
Xcm =
A block is kept on the floor of an elevator at rest. The elevator starts descending with an acceleration of 12 m/s2. Find the displacement of the block during the first 0.2 s after the start. (Take, g = 10 m/s2)
30 cm
zero
20 cm
25 cm
A rod PQ of length l is moving with ends remaining in contact with frictionless wall and floor. If at the instant, shown the velocity of end Q is 2 m/s towards negative direction of x. The speed of end P will be
The displacement x of a particle varies with time t as x = ae-αt + beβt where a, b, and β are positive constants. The velocity of the particle will
decrease with time
be independent of
drop to zero when
increase with time
If A + B = C and that C is perpendicular to A. What is the angle between A and B, if
rad
rad
rad
rad
A body is whirled in a horizontal circle of radius 25 cm. It has an angular velocity of 13 rad/s. What is its linear velocity at any point on circular path?
2 m/s
3 m/s
3.25 m/s
4.25 m/s