0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

A particle of mass m moves with the potential energy U shown above.The period of the motion when the particle has total energy E is
131405.png
  1. 2πm/k+42E/mg2
  2. 22E/mg2
  3. 2πm/k
  4. πm/k+22E/mg2

A
2πm/k
B
πm/k+22E/mg2
C
22E/mg2
D
2πm/k+42E/mg2
Solution
Verified by Toppr



As seen from graph, we can infer that for x<0 particle is in SHM as in spring. and for x>0 particle is in influence of gravity i.e. thrown upwards with some initial velocity.
So we can divide the time period in two parts. first T1 and second T2
T1 is half of the time period of a full SHM i.e. T1=πmk
E=12mvmax2vmax=2Em
and T2 is the time during which the particle remains in air when it is thrown upwards with velocity vmax=2Em
0=2Emt12gt2 Since s=ut12gt2
T2=22E/mg2
So total time time period T=πmk+22Emg2

Was this answer helpful?
9
Similar Questions
Q1
A particle of mass m moves with the potential energy U shown above.The period of the motion when the particle has total energy E is
131405.png
View Solution
Q2
The potential energy of particle of mass 'm' is given by U=12kx2 for x<0 and U = 0 for x 0. If total mechanical energy of the particle is E. Then its speed at x=2Ek is
View Solution
Q3
The potential energy of particle of mass 'm' is given by U=12kx2 for x<0 and U = 0 for x 0. If total mechanical energy of the particle is E. Then its speed at x=2Ek is
View Solution
Q4
The potential energy of a particle of mass m is givenU=12kx2 for x < 0 and U = 0 for x0. if total mechanical energy of the particle is E, then its speed at x=2Ek is
View Solution
Q5
The potential energy of a particle of mass m free to move along x-axis is given by U=12kx2 for x<0 and U=0 for x0 (x denotes the x-coordinate of the particle and k is a positive constant). If the total mechanical energy of the particle is E, then its speed at x=2Ek is :
View Solution