Two bodies of mass $10 \, kg$ and $5 \, kg$ are moving in concentric orbits of radii $R$ and $r$ such that their periods are the same. What is the ratio of their centripetal accelerations?

$A$ body moves along a circular path of radius $100 \,m$ and completes one revolution in $40 \,sec$. What is the total distance covered at the end of $2 \,min \,20 \,sec$ (in $\pi$)?

$A$ projectile is thrown upward at an angle $60^{\circ}$ with the horizontal. The speed of the projectile is $20 \text{ m/s}$ when its direction of motion is $45^{\circ}$ with the horizontal. The initial speed of the projectile is . . . . . . in $\text{m/s}$.

Consider a circle of radius $R = 42\ cm$. An insect crawls with a uniform speed of $v = 1.3\ cm/s$ along the chord $AB$, then along the circular arc $BCD$, and finally along the chord $DA$ to return to point $A$. The time taken by the insect to crawl from $A$ back to $A$ is closest to ......... $\sec$.

Two cars $S_1$ and $S_2$ are moving in coplanar concentric circular tracks in the opposite sense with the periods of revolution $3 \, min$ and $24 \, min$,respectively. At time $t = 0$,the cars are farthest apart. Then,the two cars will be

$A$ cart moves with a constant speed along a horizontal circular path. From the cart,a particle is thrown up vertically with respect to the cart.