04. Motion Under Gravity
Motion in One Dimensions

141817 From a \(200 \mathrm{~m}\) high tower, one ball is thrown upwards with speed of \(10 \mathrm{~ms}^{-1}\) and another is thrown vertically downwards at the same speeds simultaneously. The time difference of their reaching the ground will be nearest to

1 \(12 \mathrm{~s}\)
2 \(6 \mathrm{~s}\)
3 \(2 \mathrm{~s}\)
4 \(1 \mathrm{~s}\)
Motion in One Dimensions

141818 A ball is thrown straight upward from ground with a speed of \(20 \mathrm{~m} / \mathrm{s}\). The ball was caught on its way down at a point \(5 \mathrm{~m}\) above the ground. The time taken by the ball during entire trip is (assume, \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(2+\sqrt{3} \mathrm{~s}\)
2 \(3-\sqrt{3} \mathrm{~s}\)
3 \(2+\sqrt{2} \mathrm{~s}\)
4 \(3.5 \mathrm{~s}\)
Motion in One Dimensions

141819 A ball of mass \(100 \mathrm{~g}\) is dropped at time \(t=0\). A second ball of mass \(200 \mathrm{~g}\) is dropped from the same point at \(t=0.2 \mathrm{~s}\). The distance between the centre of mass of two balls and the release point at \(t=0.4 \mathrm{~s}\) is
(Assume, \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(0.4 \mathrm{~m}\)
2 \(0.5 \mathrm{~m}\)
3 \(0.6 \mathrm{~m}\)
4 \(0.8 \mathrm{~m}\)
Motion in One Dimensions

141820 A ball is dropped from a height \(\mathrm{H}\) from rest. The ball travels \(\frac{H}{2}\) in last \(1.0 \mathrm{~s}\). The total time taken by the ball to hit the ground is

1 \(3.85 \mathrm{~s}\)
2 \(3.41 \mathrm{~s}\)
3 \(2.55 \mathrm{~s}\)
4 \(4.65 \mathrm{~s}\)
Motion in One Dimensions

141821 A body is projected vertically upwards. The time corresponding to height \(h\) while ascending and while descending are \(t_{1}\) and \(t_{2}\) respectively. Then the velocity of projection is ( \(g\) is acceleration due to gravity)

1 \(\frac{g \sqrt{t_{1} t_{2}}}{2}\)
2 \(\frac{g\left(t_{1}+t_{2}\right)}{2}\)
3 \(g \sqrt{t_{1} t_{2}}\)
4 \(\frac{\mathrm{gt}_{1} \mathrm{t}_{2}}{\mathrm{t}_{1}+\mathrm{t}_{2}}\)
Motion in One Dimensions

141817 From a \(200 \mathrm{~m}\) high tower, one ball is thrown upwards with speed of \(10 \mathrm{~ms}^{-1}\) and another is thrown vertically downwards at the same speeds simultaneously. The time difference of their reaching the ground will be nearest to

1 \(12 \mathrm{~s}\)
2 \(6 \mathrm{~s}\)
3 \(2 \mathrm{~s}\)
4 \(1 \mathrm{~s}\)
Motion in One Dimensions

141818 A ball is thrown straight upward from ground with a speed of \(20 \mathrm{~m} / \mathrm{s}\). The ball was caught on its way down at a point \(5 \mathrm{~m}\) above the ground. The time taken by the ball during entire trip is (assume, \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(2+\sqrt{3} \mathrm{~s}\)
2 \(3-\sqrt{3} \mathrm{~s}\)
3 \(2+\sqrt{2} \mathrm{~s}\)
4 \(3.5 \mathrm{~s}\)
Motion in One Dimensions

141819 A ball of mass \(100 \mathrm{~g}\) is dropped at time \(t=0\). A second ball of mass \(200 \mathrm{~g}\) is dropped from the same point at \(t=0.2 \mathrm{~s}\). The distance between the centre of mass of two balls and the release point at \(t=0.4 \mathrm{~s}\) is
(Assume, \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(0.4 \mathrm{~m}\)
2 \(0.5 \mathrm{~m}\)
3 \(0.6 \mathrm{~m}\)
4 \(0.8 \mathrm{~m}\)
Motion in One Dimensions

141820 A ball is dropped from a height \(\mathrm{H}\) from rest. The ball travels \(\frac{H}{2}\) in last \(1.0 \mathrm{~s}\). The total time taken by the ball to hit the ground is

1 \(3.85 \mathrm{~s}\)
2 \(3.41 \mathrm{~s}\)
3 \(2.55 \mathrm{~s}\)
4 \(4.65 \mathrm{~s}\)
Motion in One Dimensions

141821 A body is projected vertically upwards. The time corresponding to height \(h\) while ascending and while descending are \(t_{1}\) and \(t_{2}\) respectively. Then the velocity of projection is ( \(g\) is acceleration due to gravity)

1 \(\frac{g \sqrt{t_{1} t_{2}}}{2}\)
2 \(\frac{g\left(t_{1}+t_{2}\right)}{2}\)
3 \(g \sqrt{t_{1} t_{2}}\)
4 \(\frac{\mathrm{gt}_{1} \mathrm{t}_{2}}{\mathrm{t}_{1}+\mathrm{t}_{2}}\)
Motion in One Dimensions

141817 From a \(200 \mathrm{~m}\) high tower, one ball is thrown upwards with speed of \(10 \mathrm{~ms}^{-1}\) and another is thrown vertically downwards at the same speeds simultaneously. The time difference of their reaching the ground will be nearest to

1 \(12 \mathrm{~s}\)
2 \(6 \mathrm{~s}\)
3 \(2 \mathrm{~s}\)
4 \(1 \mathrm{~s}\)
Motion in One Dimensions

141818 A ball is thrown straight upward from ground with a speed of \(20 \mathrm{~m} / \mathrm{s}\). The ball was caught on its way down at a point \(5 \mathrm{~m}\) above the ground. The time taken by the ball during entire trip is (assume, \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(2+\sqrt{3} \mathrm{~s}\)
2 \(3-\sqrt{3} \mathrm{~s}\)
3 \(2+\sqrt{2} \mathrm{~s}\)
4 \(3.5 \mathrm{~s}\)
Motion in One Dimensions

141819 A ball of mass \(100 \mathrm{~g}\) is dropped at time \(t=0\). A second ball of mass \(200 \mathrm{~g}\) is dropped from the same point at \(t=0.2 \mathrm{~s}\). The distance between the centre of mass of two balls and the release point at \(t=0.4 \mathrm{~s}\) is
(Assume, \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(0.4 \mathrm{~m}\)
2 \(0.5 \mathrm{~m}\)
3 \(0.6 \mathrm{~m}\)
4 \(0.8 \mathrm{~m}\)
Motion in One Dimensions

141820 A ball is dropped from a height \(\mathrm{H}\) from rest. The ball travels \(\frac{H}{2}\) in last \(1.0 \mathrm{~s}\). The total time taken by the ball to hit the ground is

1 \(3.85 \mathrm{~s}\)
2 \(3.41 \mathrm{~s}\)
3 \(2.55 \mathrm{~s}\)
4 \(4.65 \mathrm{~s}\)
Motion in One Dimensions

141821 A body is projected vertically upwards. The time corresponding to height \(h\) while ascending and while descending are \(t_{1}\) and \(t_{2}\) respectively. Then the velocity of projection is ( \(g\) is acceleration due to gravity)

1 \(\frac{g \sqrt{t_{1} t_{2}}}{2}\)
2 \(\frac{g\left(t_{1}+t_{2}\right)}{2}\)
3 \(g \sqrt{t_{1} t_{2}}\)
4 \(\frac{\mathrm{gt}_{1} \mathrm{t}_{2}}{\mathrm{t}_{1}+\mathrm{t}_{2}}\)
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Motion in One Dimensions

141817 From a \(200 \mathrm{~m}\) high tower, one ball is thrown upwards with speed of \(10 \mathrm{~ms}^{-1}\) and another is thrown vertically downwards at the same speeds simultaneously. The time difference of their reaching the ground will be nearest to

1 \(12 \mathrm{~s}\)
2 \(6 \mathrm{~s}\)
3 \(2 \mathrm{~s}\)
4 \(1 \mathrm{~s}\)
Motion in One Dimensions

141818 A ball is thrown straight upward from ground with a speed of \(20 \mathrm{~m} / \mathrm{s}\). The ball was caught on its way down at a point \(5 \mathrm{~m}\) above the ground. The time taken by the ball during entire trip is (assume, \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(2+\sqrt{3} \mathrm{~s}\)
2 \(3-\sqrt{3} \mathrm{~s}\)
3 \(2+\sqrt{2} \mathrm{~s}\)
4 \(3.5 \mathrm{~s}\)
Motion in One Dimensions

141819 A ball of mass \(100 \mathrm{~g}\) is dropped at time \(t=0\). A second ball of mass \(200 \mathrm{~g}\) is dropped from the same point at \(t=0.2 \mathrm{~s}\). The distance between the centre of mass of two balls and the release point at \(t=0.4 \mathrm{~s}\) is
(Assume, \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(0.4 \mathrm{~m}\)
2 \(0.5 \mathrm{~m}\)
3 \(0.6 \mathrm{~m}\)
4 \(0.8 \mathrm{~m}\)
Motion in One Dimensions

141820 A ball is dropped from a height \(\mathrm{H}\) from rest. The ball travels \(\frac{H}{2}\) in last \(1.0 \mathrm{~s}\). The total time taken by the ball to hit the ground is

1 \(3.85 \mathrm{~s}\)
2 \(3.41 \mathrm{~s}\)
3 \(2.55 \mathrm{~s}\)
4 \(4.65 \mathrm{~s}\)
Motion in One Dimensions

141821 A body is projected vertically upwards. The time corresponding to height \(h\) while ascending and while descending are \(t_{1}\) and \(t_{2}\) respectively. Then the velocity of projection is ( \(g\) is acceleration due to gravity)

1 \(\frac{g \sqrt{t_{1} t_{2}}}{2}\)
2 \(\frac{g\left(t_{1}+t_{2}\right)}{2}\)
3 \(g \sqrt{t_{1} t_{2}}\)
4 \(\frac{\mathrm{gt}_{1} \mathrm{t}_{2}}{\mathrm{t}_{1}+\mathrm{t}_{2}}\)
Motion in One Dimensions

141817 From a \(200 \mathrm{~m}\) high tower, one ball is thrown upwards with speed of \(10 \mathrm{~ms}^{-1}\) and another is thrown vertically downwards at the same speeds simultaneously. The time difference of their reaching the ground will be nearest to

1 \(12 \mathrm{~s}\)
2 \(6 \mathrm{~s}\)
3 \(2 \mathrm{~s}\)
4 \(1 \mathrm{~s}\)
Motion in One Dimensions

141818 A ball is thrown straight upward from ground with a speed of \(20 \mathrm{~m} / \mathrm{s}\). The ball was caught on its way down at a point \(5 \mathrm{~m}\) above the ground. The time taken by the ball during entire trip is (assume, \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(2+\sqrt{3} \mathrm{~s}\)
2 \(3-\sqrt{3} \mathrm{~s}\)
3 \(2+\sqrt{2} \mathrm{~s}\)
4 \(3.5 \mathrm{~s}\)
Motion in One Dimensions

141819 A ball of mass \(100 \mathrm{~g}\) is dropped at time \(t=0\). A second ball of mass \(200 \mathrm{~g}\) is dropped from the same point at \(t=0.2 \mathrm{~s}\). The distance between the centre of mass of two balls and the release point at \(t=0.4 \mathrm{~s}\) is
(Assume, \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(0.4 \mathrm{~m}\)
2 \(0.5 \mathrm{~m}\)
3 \(0.6 \mathrm{~m}\)
4 \(0.8 \mathrm{~m}\)
Motion in One Dimensions

141820 A ball is dropped from a height \(\mathrm{H}\) from rest. The ball travels \(\frac{H}{2}\) in last \(1.0 \mathrm{~s}\). The total time taken by the ball to hit the ground is

1 \(3.85 \mathrm{~s}\)
2 \(3.41 \mathrm{~s}\)
3 \(2.55 \mathrm{~s}\)
4 \(4.65 \mathrm{~s}\)
Motion in One Dimensions

141821 A body is projected vertically upwards. The time corresponding to height \(h\) while ascending and while descending are \(t_{1}\) and \(t_{2}\) respectively. Then the velocity of projection is ( \(g\) is acceleration due to gravity)

1 \(\frac{g \sqrt{t_{1} t_{2}}}{2}\)
2 \(\frac{g\left(t_{1}+t_{2}\right)}{2}\)
3 \(g \sqrt{t_{1} t_{2}}\)
4 \(\frac{\mathrm{gt}_{1} \mathrm{t}_{2}}{\mathrm{t}_{1}+\mathrm{t}_{2}}\)