04. Motion Under Gravity
Motion in One Dimensions

141822 A ball of mass \(200 \mathrm{~g}\) is thrown directly upward from \(X\)-axis from \(x=2 \mathrm{~m}\) position. The initial speed of the ball is \(40 \mathrm{~m} / \mathrm{s}\). The magnitude (absolute value) of the angular momentum of the ball about the origin \((x=0)\), when ball is halfway back to the ground is:

1 \(8 \mathrm{~N} . \mathrm{m}\)
2 16 N.m
3 \(8 \sqrt{2} \mathrm{~N} \cdot \mathrm{m}\)
4 \(16 \sqrt{2} \mathrm{~N} \cdot \mathrm{m}\)
Motion in One Dimensions

141823 A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height \(h\). The time taken by the packet to reach the ground is close to (Here, \(g\) is the acceleration due to gravity).

1 \(\mathrm{t}=\frac{2}{3} \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\)
2 \(\mathrm{t}=1.8 \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\)
3 \(\mathrm{t}=\sqrt{\frac{2 \mathrm{~h}}{3 \mathrm{~g}}}\)
4 \(t=3.4 \sqrt{\frac{h}{g}}\)
Motion in One Dimensions

141824 A ball is dropped from a bridge that is \(45 \mathrm{~m}\) above the water. It falls directly into a boat which is moving with constant velocity. The boat is \(12 \mathrm{~m}\) away from the point of impact when the ball is dropped. The speed of the boat is \(\left(\right.\) take, \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(2 \mathrm{~m} / \mathrm{s}\)
2 \(3 \mathrm{~m} / \mathrm{s}\)
3 \(4 \mathrm{~m} / \mathrm{s}\)
4 \(5 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141825 A man in a lift ascending with an acceleration throws a ball vertically up with a velocity \(v\) and catches it after time 3 sec. Afterwards when the lift is descending with the same acceleration, the man again throws the ball vertically up with the same velocity and catches it after 1 sec. Find \(v\) (use \(g=10 \mathrm{~m} / \mathrm{s}\) ).

1 \(7.5 \mathrm{~m} / \mathrm{s}\)
2 \(9.0 \mathrm{~m} / \mathrm{s}\)
3 \(10.5 \mathrm{~m} / \mathrm{s}\)
4 \(12.5 \mathrm{~m} / \mathrm{s}\)
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Motion in One Dimensions

141822 A ball of mass \(200 \mathrm{~g}\) is thrown directly upward from \(X\)-axis from \(x=2 \mathrm{~m}\) position. The initial speed of the ball is \(40 \mathrm{~m} / \mathrm{s}\). The magnitude (absolute value) of the angular momentum of the ball about the origin \((x=0)\), when ball is halfway back to the ground is:

1 \(8 \mathrm{~N} . \mathrm{m}\)
2 16 N.m
3 \(8 \sqrt{2} \mathrm{~N} \cdot \mathrm{m}\)
4 \(16 \sqrt{2} \mathrm{~N} \cdot \mathrm{m}\)
Motion in One Dimensions

141823 A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height \(h\). The time taken by the packet to reach the ground is close to (Here, \(g\) is the acceleration due to gravity).

1 \(\mathrm{t}=\frac{2}{3} \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\)
2 \(\mathrm{t}=1.8 \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\)
3 \(\mathrm{t}=\sqrt{\frac{2 \mathrm{~h}}{3 \mathrm{~g}}}\)
4 \(t=3.4 \sqrt{\frac{h}{g}}\)
Motion in One Dimensions

141824 A ball is dropped from a bridge that is \(45 \mathrm{~m}\) above the water. It falls directly into a boat which is moving with constant velocity. The boat is \(12 \mathrm{~m}\) away from the point of impact when the ball is dropped. The speed of the boat is \(\left(\right.\) take, \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(2 \mathrm{~m} / \mathrm{s}\)
2 \(3 \mathrm{~m} / \mathrm{s}\)
3 \(4 \mathrm{~m} / \mathrm{s}\)
4 \(5 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141825 A man in a lift ascending with an acceleration throws a ball vertically up with a velocity \(v\) and catches it after time 3 sec. Afterwards when the lift is descending with the same acceleration, the man again throws the ball vertically up with the same velocity and catches it after 1 sec. Find \(v\) (use \(g=10 \mathrm{~m} / \mathrm{s}\) ).

1 \(7.5 \mathrm{~m} / \mathrm{s}\)
2 \(9.0 \mathrm{~m} / \mathrm{s}\)
3 \(10.5 \mathrm{~m} / \mathrm{s}\)
4 \(12.5 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141822 A ball of mass \(200 \mathrm{~g}\) is thrown directly upward from \(X\)-axis from \(x=2 \mathrm{~m}\) position. The initial speed of the ball is \(40 \mathrm{~m} / \mathrm{s}\). The magnitude (absolute value) of the angular momentum of the ball about the origin \((x=0)\), when ball is halfway back to the ground is:

1 \(8 \mathrm{~N} . \mathrm{m}\)
2 16 N.m
3 \(8 \sqrt{2} \mathrm{~N} \cdot \mathrm{m}\)
4 \(16 \sqrt{2} \mathrm{~N} \cdot \mathrm{m}\)
Motion in One Dimensions

141823 A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height \(h\). The time taken by the packet to reach the ground is close to (Here, \(g\) is the acceleration due to gravity).

1 \(\mathrm{t}=\frac{2}{3} \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\)
2 \(\mathrm{t}=1.8 \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\)
3 \(\mathrm{t}=\sqrt{\frac{2 \mathrm{~h}}{3 \mathrm{~g}}}\)
4 \(t=3.4 \sqrt{\frac{h}{g}}\)
Motion in One Dimensions

141824 A ball is dropped from a bridge that is \(45 \mathrm{~m}\) above the water. It falls directly into a boat which is moving with constant velocity. The boat is \(12 \mathrm{~m}\) away from the point of impact when the ball is dropped. The speed of the boat is \(\left(\right.\) take, \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(2 \mathrm{~m} / \mathrm{s}\)
2 \(3 \mathrm{~m} / \mathrm{s}\)
3 \(4 \mathrm{~m} / \mathrm{s}\)
4 \(5 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141825 A man in a lift ascending with an acceleration throws a ball vertically up with a velocity \(v\) and catches it after time 3 sec. Afterwards when the lift is descending with the same acceleration, the man again throws the ball vertically up with the same velocity and catches it after 1 sec. Find \(v\) (use \(g=10 \mathrm{~m} / \mathrm{s}\) ).

1 \(7.5 \mathrm{~m} / \mathrm{s}\)
2 \(9.0 \mathrm{~m} / \mathrm{s}\)
3 \(10.5 \mathrm{~m} / \mathrm{s}\)
4 \(12.5 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141822 A ball of mass \(200 \mathrm{~g}\) is thrown directly upward from \(X\)-axis from \(x=2 \mathrm{~m}\) position. The initial speed of the ball is \(40 \mathrm{~m} / \mathrm{s}\). The magnitude (absolute value) of the angular momentum of the ball about the origin \((x=0)\), when ball is halfway back to the ground is:

1 \(8 \mathrm{~N} . \mathrm{m}\)
2 16 N.m
3 \(8 \sqrt{2} \mathrm{~N} \cdot \mathrm{m}\)
4 \(16 \sqrt{2} \mathrm{~N} \cdot \mathrm{m}\)
Motion in One Dimensions

141823 A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height \(h\). The time taken by the packet to reach the ground is close to (Here, \(g\) is the acceleration due to gravity).

1 \(\mathrm{t}=\frac{2}{3} \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\)
2 \(\mathrm{t}=1.8 \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\)
3 \(\mathrm{t}=\sqrt{\frac{2 \mathrm{~h}}{3 \mathrm{~g}}}\)
4 \(t=3.4 \sqrt{\frac{h}{g}}\)
Motion in One Dimensions

141824 A ball is dropped from a bridge that is \(45 \mathrm{~m}\) above the water. It falls directly into a boat which is moving with constant velocity. The boat is \(12 \mathrm{~m}\) away from the point of impact when the ball is dropped. The speed of the boat is \(\left(\right.\) take, \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(2 \mathrm{~m} / \mathrm{s}\)
2 \(3 \mathrm{~m} / \mathrm{s}\)
3 \(4 \mathrm{~m} / \mathrm{s}\)
4 \(5 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141825 A man in a lift ascending with an acceleration throws a ball vertically up with a velocity \(v\) and catches it after time 3 sec. Afterwards when the lift is descending with the same acceleration, the man again throws the ball vertically up with the same velocity and catches it after 1 sec. Find \(v\) (use \(g=10 \mathrm{~m} / \mathrm{s}\) ).

1 \(7.5 \mathrm{~m} / \mathrm{s}\)
2 \(9.0 \mathrm{~m} / \mathrm{s}\)
3 \(10.5 \mathrm{~m} / \mathrm{s}\)
4 \(12.5 \mathrm{~m} / \mathrm{s}\)