Gravitational Field Due to a Ring

Q.

A ball of mass $m$ moving with a speed $u$ collides elastically with another identical ball moving with velocity $u_2$. Find the angle between velocities after collision if they collide obliquely and $u_2$ = 0​

1. $\pi$

2. $\frac{\pi }{2}$

3. $\frac{\pi }{4}$

4. zero

Q.

A cannon ball is fired with a velocity 200 m/sec at an angle of ${60}^{\circ }$ with the horizontal. At the highest point of its flight it explodes into 3 equal fragments, one going vertically upwards with a velocity 100 m/sec, the second one falling vertically downwards with a velocity 100 m/sec. The third fragment will be moving with a velocity

1. 100 m/s in the horizontal direction

2. 300 m/s in the horizontal direction

3. 300 m/s in a direction making an angle of ${60}^{\circ }$ with the horizontal

4. 200 m/s in a direction making an angle of ${60}^{\circ }$ with the horizontal

Q. An alpha particle collides elastically with a stationary nucleus and continues moving at an angle of ${60}^{\circ }$ with respect to the original direction of motion. The nucleus recoils at an angle of ${30}^{\circ }$ with respect to initial direction of motion of alpha particle. Mass number of the nucleus is:

Q. A particle of mass $m$ moving eastwards with a speed $v$ collides with another particle of same mass moving northwards with same speed $v$. The two particles coalesces on collision. Then, the new particle of mass $2m$ will move with velocity:

1. $\frac{v}{2}\text{North-East}$
2. $\frac{v}{\sqrt{2}}\text{South-West}$
3. $\frac{v}{2}\text{North-West}$
4. $\frac{v}{\sqrt{2}}\text{North-East}$

Q. A uniform ring and uniform sphere are placed as shown in the figure. The gravitational attraction between the sphere and ring ($d=\sqrt{3}R$) is.

1. $\frac{8G{M}^2}{R^2}$
2. $\frac{2G{M}^2}{R^2}$
3. $\frac{3G{M}^2}{2R^2}$
4. $\frac{\sqrt{3}G{M}^2}{R^2}$