The period of revolution (t) of a planet moving round the sun in a circular orbit depends upon the radius (r) of the orbit, mass of

the sun (M) and gravitational constant (G). Show

dimensionally that t² x R³, hence find the numerical value of t

if r= 6.4 μm, M=2000km, G= 6.67 x 10-11Nm²kg ²,

constant of proportionality = 0.5​

Two particles of masses m and 2m are placed on a smooth horizontal table. a string, which joins these two masses, hangs over the edge supporting a pulley, which suspends a particle of mass 3m.the pulley has negligible mass. the two parts of the string on the table are parallel and perpendicular to the edge of the table. the hanging parts of the string are vertical. find the acceleration of the particle of mass 3m.

Aparticle initially moving east with a speed of 20.0 m/s, experiences an acceleration of 3.95 m/s, north for a time of 8.00 s. what was the speed of the particle after this acceleration, in units of m/s? give the answer as a positive number.

Consider a system to be two train cars traveling toward each other. what is the total momentum of the system before the train cars collide?   kg • what must the total momentum of the system be after the train cars collide?   kg •