Estimate how long a galaxy in the coma cluster would take to travel from one side of the
cluster to the other. assume that the galaxy moves with a constant speed equal to the cluster’s
radial velocity dispersion. how does this compare with the hubble time, th ? what can you
conclude about whether the galaxies in the coma cluster are gravitationally bound?

The dipole moment of the water molecule (h2o) is 6.17x10^-30 c.m. consider a water molecule located at the origin whose dipole moment p points in the +x-direction. a chlorine ion ( of charge-1.60x10^-19c , is located at x=3.00x10^-9m . assume that is much larger than the separation d between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis can be used. a) find the magnitude of the electric force that the water molecule exerts on the chlorine ion. b) what is the direction of the electric force. -x-direction or +x-direction c) is this force attractive or repulsive?