COLLISIONS
Work, Energy and Power

268913 A particle strikes a horizontal frictionless floor with a speed ' \(u\) ' at an angle ' \(\theta\) ' with the vertical and rebounds with a speed ' \(v\) ' at an angle ' \(\alpha\) ' with the vertical. Find the value of ' \(v\) ' if ' \(\mathbf{e}\) ' is the coefficient of restitution.

1 \(\mathrm{v}=\mathrm{u} \sqrt{\mathrm{e}^{2} \sin ^{2} \theta+\cos ^{2} \theta}\)
2 \(v=\mathrm{l} \sqrt{\mathrm{e}^{2} \cos ^{2} \theta+\sin ^{2} \theta}\)
3 \(\mathrm{v}=\sqrt{\mathrm{e}^{2} \cos ^{2} \theta+\tan ^{2} \theta}\)
4 \({v}=u \sqrt{\cot ^{2} \theta+e^{2} \cos ^{2} \theta}\)
Work, Energy and Power

268914 Two spheres \(A\) and \(B\) of equal masses lie on the smooth horizontal circular groove at opposite ends of diameter and at the end of time ' \(t\) ', ' \(A\) ' impinges on ' \(B\) '. If ' \(e\) ' is the coefficient of restitution, the second impinge will occur after a time

1 \(\frac{2 t}{e}\)
2 \(\frac{t}{e}\)
3 \(\frac{\pi t}{e}\)
4 \(\frac{2 \pi t}{e}\)
Work, Energy and Power

268915 A ball is thrown at an angle of incidence ' \(\theta\) ' on a horizontal plane such that the incident direction and the reflected direction are at right angles to each other. If the coefficient of restitution is ' \(\mathbf{e}\) ' then ' \(\theta\) ' is equal to

1 \(\tan ^{-1}(\mathrm{e})\)
2 \(\tan ^{-1}(2 e)\)
3 \(\tan ^{-1}(\sqrt{2} e)\)
4 \(\tan ^{-1}(\sqrt{\mathrm{e}})\)
Work, Energy and Power

268916 Consider the collision depicted in fig to be between two billiard balls with equal masses \(m_{1}=m_{2}\). The first ball is called the target. The billiard player wants to 'sink' the target ball in a corner pocket, which is at an angle \(\theta_{2}=37^{\circ}\). Assume that the collision is elastic and that friction and rotational motion are not important, then \(\theta_{1}\) is

1 \(37^{\circ}\)
2 \(90^{\circ}\)
3 \(45^{\circ}\)
4 \(53^{\circ}\)
Work, Energy and Power

268917 A projectile is fixed on a horizontal ground. Coefficient of restitution between the projectile and the ground is ' \(e\) '. If \(a, b\) and \(c\) be the ratio of time of flight \(\frac{\left.\square T_{1}\right]}{\square T_{2}} \frac{\square}{\square}\), maximum height \(\left.\frac{\square H_{1}}{\left[\mathrm{H}_{2}\right.}\right]\) and horizontal range \(\frac{\square R_{1}}{\square R_{2}}\). two collisions with the ground, then

1 \(a=\frac{1}{e}\)
2 \(b=\frac{1}{e^{2}}\)
3 \(c=\frac{1}{e}\)
4 \(1,2 \& 3\)
Work, Energy and Power

268913 A particle strikes a horizontal frictionless floor with a speed ' \(u\) ' at an angle ' \(\theta\) ' with the vertical and rebounds with a speed ' \(v\) ' at an angle ' \(\alpha\) ' with the vertical. Find the value of ' \(v\) ' if ' \(\mathbf{e}\) ' is the coefficient of restitution.

1 \(\mathrm{v}=\mathrm{u} \sqrt{\mathrm{e}^{2} \sin ^{2} \theta+\cos ^{2} \theta}\)
2 \(v=\mathrm{l} \sqrt{\mathrm{e}^{2} \cos ^{2} \theta+\sin ^{2} \theta}\)
3 \(\mathrm{v}=\sqrt{\mathrm{e}^{2} \cos ^{2} \theta+\tan ^{2} \theta}\)
4 \({v}=u \sqrt{\cot ^{2} \theta+e^{2} \cos ^{2} \theta}\)
Work, Energy and Power

268914 Two spheres \(A\) and \(B\) of equal masses lie on the smooth horizontal circular groove at opposite ends of diameter and at the end of time ' \(t\) ', ' \(A\) ' impinges on ' \(B\) '. If ' \(e\) ' is the coefficient of restitution, the second impinge will occur after a time

1 \(\frac{2 t}{e}\)
2 \(\frac{t}{e}\)
3 \(\frac{\pi t}{e}\)
4 \(\frac{2 \pi t}{e}\)
Work, Energy and Power

268915 A ball is thrown at an angle of incidence ' \(\theta\) ' on a horizontal plane such that the incident direction and the reflected direction are at right angles to each other. If the coefficient of restitution is ' \(\mathbf{e}\) ' then ' \(\theta\) ' is equal to

1 \(\tan ^{-1}(\mathrm{e})\)
2 \(\tan ^{-1}(2 e)\)
3 \(\tan ^{-1}(\sqrt{2} e)\)
4 \(\tan ^{-1}(\sqrt{\mathrm{e}})\)
Work, Energy and Power

268916 Consider the collision depicted in fig to be between two billiard balls with equal masses \(m_{1}=m_{2}\). The first ball is called the target. The billiard player wants to 'sink' the target ball in a corner pocket, which is at an angle \(\theta_{2}=37^{\circ}\). Assume that the collision is elastic and that friction and rotational motion are not important, then \(\theta_{1}\) is

1 \(37^{\circ}\)
2 \(90^{\circ}\)
3 \(45^{\circ}\)
4 \(53^{\circ}\)
Work, Energy and Power

268917 A projectile is fixed on a horizontal ground. Coefficient of restitution between the projectile and the ground is ' \(e\) '. If \(a, b\) and \(c\) be the ratio of time of flight \(\frac{\left.\square T_{1}\right]}{\square T_{2}} \frac{\square}{\square}\), maximum height \(\left.\frac{\square H_{1}}{\left[\mathrm{H}_{2}\right.}\right]\) and horizontal range \(\frac{\square R_{1}}{\square R_{2}}\). two collisions with the ground, then

1 \(a=\frac{1}{e}\)
2 \(b=\frac{1}{e^{2}}\)
3 \(c=\frac{1}{e}\)
4 \(1,2 \& 3\)
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Work, Energy and Power

268913 A particle strikes a horizontal frictionless floor with a speed ' \(u\) ' at an angle ' \(\theta\) ' with the vertical and rebounds with a speed ' \(v\) ' at an angle ' \(\alpha\) ' with the vertical. Find the value of ' \(v\) ' if ' \(\mathbf{e}\) ' is the coefficient of restitution.

1 \(\mathrm{v}=\mathrm{u} \sqrt{\mathrm{e}^{2} \sin ^{2} \theta+\cos ^{2} \theta}\)
2 \(v=\mathrm{l} \sqrt{\mathrm{e}^{2} \cos ^{2} \theta+\sin ^{2} \theta}\)
3 \(\mathrm{v}=\sqrt{\mathrm{e}^{2} \cos ^{2} \theta+\tan ^{2} \theta}\)
4 \({v}=u \sqrt{\cot ^{2} \theta+e^{2} \cos ^{2} \theta}\)
Work, Energy and Power

268914 Two spheres \(A\) and \(B\) of equal masses lie on the smooth horizontal circular groove at opposite ends of diameter and at the end of time ' \(t\) ', ' \(A\) ' impinges on ' \(B\) '. If ' \(e\) ' is the coefficient of restitution, the second impinge will occur after a time

1 \(\frac{2 t}{e}\)
2 \(\frac{t}{e}\)
3 \(\frac{\pi t}{e}\)
4 \(\frac{2 \pi t}{e}\)
Work, Energy and Power

268915 A ball is thrown at an angle of incidence ' \(\theta\) ' on a horizontal plane such that the incident direction and the reflected direction are at right angles to each other. If the coefficient of restitution is ' \(\mathbf{e}\) ' then ' \(\theta\) ' is equal to

1 \(\tan ^{-1}(\mathrm{e})\)
2 \(\tan ^{-1}(2 e)\)
3 \(\tan ^{-1}(\sqrt{2} e)\)
4 \(\tan ^{-1}(\sqrt{\mathrm{e}})\)
Work, Energy and Power

268916 Consider the collision depicted in fig to be between two billiard balls with equal masses \(m_{1}=m_{2}\). The first ball is called the target. The billiard player wants to 'sink' the target ball in a corner pocket, which is at an angle \(\theta_{2}=37^{\circ}\). Assume that the collision is elastic and that friction and rotational motion are not important, then \(\theta_{1}\) is

1 \(37^{\circ}\)
2 \(90^{\circ}\)
3 \(45^{\circ}\)
4 \(53^{\circ}\)
Work, Energy and Power

268917 A projectile is fixed on a horizontal ground. Coefficient of restitution between the projectile and the ground is ' \(e\) '. If \(a, b\) and \(c\) be the ratio of time of flight \(\frac{\left.\square T_{1}\right]}{\square T_{2}} \frac{\square}{\square}\), maximum height \(\left.\frac{\square H_{1}}{\left[\mathrm{H}_{2}\right.}\right]\) and horizontal range \(\frac{\square R_{1}}{\square R_{2}}\). two collisions with the ground, then

1 \(a=\frac{1}{e}\)
2 \(b=\frac{1}{e^{2}}\)
3 \(c=\frac{1}{e}\)
4 \(1,2 \& 3\)
Work, Energy and Power

268913 A particle strikes a horizontal frictionless floor with a speed ' \(u\) ' at an angle ' \(\theta\) ' with the vertical and rebounds with a speed ' \(v\) ' at an angle ' \(\alpha\) ' with the vertical. Find the value of ' \(v\) ' if ' \(\mathbf{e}\) ' is the coefficient of restitution.

1 \(\mathrm{v}=\mathrm{u} \sqrt{\mathrm{e}^{2} \sin ^{2} \theta+\cos ^{2} \theta}\)
2 \(v=\mathrm{l} \sqrt{\mathrm{e}^{2} \cos ^{2} \theta+\sin ^{2} \theta}\)
3 \(\mathrm{v}=\sqrt{\mathrm{e}^{2} \cos ^{2} \theta+\tan ^{2} \theta}\)
4 \({v}=u \sqrt{\cot ^{2} \theta+e^{2} \cos ^{2} \theta}\)
Work, Energy and Power

268914 Two spheres \(A\) and \(B\) of equal masses lie on the smooth horizontal circular groove at opposite ends of diameter and at the end of time ' \(t\) ', ' \(A\) ' impinges on ' \(B\) '. If ' \(e\) ' is the coefficient of restitution, the second impinge will occur after a time

1 \(\frac{2 t}{e}\)
2 \(\frac{t}{e}\)
3 \(\frac{\pi t}{e}\)
4 \(\frac{2 \pi t}{e}\)
Work, Energy and Power

268915 A ball is thrown at an angle of incidence ' \(\theta\) ' on a horizontal plane such that the incident direction and the reflected direction are at right angles to each other. If the coefficient of restitution is ' \(\mathbf{e}\) ' then ' \(\theta\) ' is equal to

1 \(\tan ^{-1}(\mathrm{e})\)
2 \(\tan ^{-1}(2 e)\)
3 \(\tan ^{-1}(\sqrt{2} e)\)
4 \(\tan ^{-1}(\sqrt{\mathrm{e}})\)
Work, Energy and Power

268916 Consider the collision depicted in fig to be between two billiard balls with equal masses \(m_{1}=m_{2}\). The first ball is called the target. The billiard player wants to 'sink' the target ball in a corner pocket, which is at an angle \(\theta_{2}=37^{\circ}\). Assume that the collision is elastic and that friction and rotational motion are not important, then \(\theta_{1}\) is

1 \(37^{\circ}\)
2 \(90^{\circ}\)
3 \(45^{\circ}\)
4 \(53^{\circ}\)
Work, Energy and Power

268917 A projectile is fixed on a horizontal ground. Coefficient of restitution between the projectile and the ground is ' \(e\) '. If \(a, b\) and \(c\) be the ratio of time of flight \(\frac{\left.\square T_{1}\right]}{\square T_{2}} \frac{\square}{\square}\), maximum height \(\left.\frac{\square H_{1}}{\left[\mathrm{H}_{2}\right.}\right]\) and horizontal range \(\frac{\square R_{1}}{\square R_{2}}\). two collisions with the ground, then

1 \(a=\frac{1}{e}\)
2 \(b=\frac{1}{e^{2}}\)
3 \(c=\frac{1}{e}\)
4 \(1,2 \& 3\)
Work, Energy and Power

268913 A particle strikes a horizontal frictionless floor with a speed ' \(u\) ' at an angle ' \(\theta\) ' with the vertical and rebounds with a speed ' \(v\) ' at an angle ' \(\alpha\) ' with the vertical. Find the value of ' \(v\) ' if ' \(\mathbf{e}\) ' is the coefficient of restitution.

1 \(\mathrm{v}=\mathrm{u} \sqrt{\mathrm{e}^{2} \sin ^{2} \theta+\cos ^{2} \theta}\)
2 \(v=\mathrm{l} \sqrt{\mathrm{e}^{2} \cos ^{2} \theta+\sin ^{2} \theta}\)
3 \(\mathrm{v}=\sqrt{\mathrm{e}^{2} \cos ^{2} \theta+\tan ^{2} \theta}\)
4 \({v}=u \sqrt{\cot ^{2} \theta+e^{2} \cos ^{2} \theta}\)
Work, Energy and Power

268914 Two spheres \(A\) and \(B\) of equal masses lie on the smooth horizontal circular groove at opposite ends of diameter and at the end of time ' \(t\) ', ' \(A\) ' impinges on ' \(B\) '. If ' \(e\) ' is the coefficient of restitution, the second impinge will occur after a time

1 \(\frac{2 t}{e}\)
2 \(\frac{t}{e}\)
3 \(\frac{\pi t}{e}\)
4 \(\frac{2 \pi t}{e}\)
Work, Energy and Power

268915 A ball is thrown at an angle of incidence ' \(\theta\) ' on a horizontal plane such that the incident direction and the reflected direction are at right angles to each other. If the coefficient of restitution is ' \(\mathbf{e}\) ' then ' \(\theta\) ' is equal to

1 \(\tan ^{-1}(\mathrm{e})\)
2 \(\tan ^{-1}(2 e)\)
3 \(\tan ^{-1}(\sqrt{2} e)\)
4 \(\tan ^{-1}(\sqrt{\mathrm{e}})\)
Work, Energy and Power

268916 Consider the collision depicted in fig to be between two billiard balls with equal masses \(m_{1}=m_{2}\). The first ball is called the target. The billiard player wants to 'sink' the target ball in a corner pocket, which is at an angle \(\theta_{2}=37^{\circ}\). Assume that the collision is elastic and that friction and rotational motion are not important, then \(\theta_{1}\) is

1 \(37^{\circ}\)
2 \(90^{\circ}\)
3 \(45^{\circ}\)
4 \(53^{\circ}\)
Work, Energy and Power

268917 A projectile is fixed on a horizontal ground. Coefficient of restitution between the projectile and the ground is ' \(e\) '. If \(a, b\) and \(c\) be the ratio of time of flight \(\frac{\left.\square T_{1}\right]}{\square T_{2}} \frac{\square}{\square}\), maximum height \(\left.\frac{\square H_{1}}{\left[\mathrm{H}_{2}\right.}\right]\) and horizontal range \(\frac{\square R_{1}}{\square R_{2}}\). two collisions with the ground, then

1 \(a=\frac{1}{e}\)
2 \(b=\frac{1}{e^{2}}\)
3 \(c=\frac{1}{e}\)
4 \(1,2 \& 3\)