The length of the seconds pendulum is 1 ~m on earth. If the mass and diameter of the planet is 1.5 times that of the earth, the length of the seconds pendulum on the planet will be nearly

Step-by-step solution

If g is the acceleration due to gravity on earth's surface and g' on the planet, then aligned & g = GM r ^2 and g ^ = G 1.5 M (1.5)^2 r ^2 = 1 1.5 GM r ^2 & g ^ = g 1.5 aligned For second's pendulum T =2 ~s aligned & T =2 g =2 ^ g ^ & g = ^ g ^ aligned ^ = g ^ g =1 1 1.5 = 2 3 =0.67 ~m