The displacement of a particle executing $SHM$ is given by $y=5 \sin \left(4 t+\frac{\pi}{3}\right)$. If $T$ is the time period and the mass of the particle is $2 \text{ g}$,the kinetic energy of the particle when $t=\frac{T}{4}$ is given by (in $J$)

Particles of masses $m, 2m, 3m, \dots, nm$ grams are placed on the same line at distances $l, 2l, 3l, \dots, nl$ cm from a fixed point. The distance of the centre of mass of the particles from the fixed point in centimetres is:

$IPM$ (Integrated Pest Management) involves

$A$ cylinder of height $h$ is filled with water and is kept on a block of height $h / 2$. The level of water in the cylinder is kept constant. Four holes numbered $1, 2, 3$ and $4$ are at the side of the cylinder and at heights $0, h / 4, h / 2$ and $3h / 4$ respectively from the base of the cylinder. When all four holes are opened together,the hole from which water will reach the farthest distance on the plane $PQ$ is the hole number

In a playground,there is a merry-go-round of mass $120 \ kg$ and radius $4 \ m$. The radius of gyration is $3 \ m$. $A$ child of mass $30 \ kg$ runs at a speed of $5 \ m/s$ tangent to the rim of the merry-go-round when it is at rest and then jumps on it. Neglecting friction,find the angular velocity of the merry-go-round and child in $rad/s$.

The species having a bond order different from that in $CO$ is