MOTION IN A PLANE
Motion in Plane

269946 The displacement of the point of a wheel initially in contact with the ground when the wheel rolls forward quarter revolution where perimeter of the wheel is \(4 \pi \mathrm{m}\), is (Assume the forward direction as \(\mathrm{x}\)-axis)

1 \(\sqrt{(\pi+2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi}\) with \(x\) - axis
2 \(\sqrt{(\pi-2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi-2}\) with \(x\) - axis
3 \(\sqrt{(\pi-2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi}\) with \(x\) - axis
4 \(\sqrt{(\pi+2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi-2}\) with \(x\) - axis
Motion in Plane

269947 A particle starts from the origin at \(t=0 \mathrm{~s}\) with a velocity of \(10.0 \hat{j} \mathbf{~ m} / \mathrm{s}\) and moves in the \(x y\)-plane with a constant acceleration of \((8 \hat{i}+2 \hat{j}) \mathrm{ms}^{-2}\). Then \(y\)-coordinate of the particle in \(2 \mathrm{sec}\) is

1 \(24 \mathrm{~m}\)
2 \(16 \mathrm{~m}\)
3 \(8 \mathrm{~m}\)
4 \(12 \mathrm{~m}\)
Motion in Plane

269948 A car moving at a constant speed of \(36 \mathrm{kmph}\) moves north wards for 20 minutes then due to west with the same speed for \(8 \frac{1}{3}\) minutes. what is the average velocity of the car during this run in \(\mathbf{k m p h}\)

1 27.5
2 40.5
3 20.8
4 32.7
Motion in Plane

269949 Velocity of a particle at time \(t=0\) is \(2 \mathrm{~ms}^{-1}\). A constant acceleration of \(2 \mathrm{~ms}^{-2}\) acts on the particle for 1 second at an angle of \(60^{\circ}\) with its initial velocity. Find the magnitude of velocity at the end of 1 second.

1 \(\sqrt{3} \mathrm{~m} / \mathrm{s}\)
2 \(2 \sqrt{3} \mathrm{~m} / \mathrm{s}\)
3 \(4 \mathrm{~m} / \mathrm{s}\)
4 \(8 \mathrm{~m} / \mathrm{s}\)
Motion in Plane

269946 The displacement of the point of a wheel initially in contact with the ground when the wheel rolls forward quarter revolution where perimeter of the wheel is \(4 \pi \mathrm{m}\), is (Assume the forward direction as \(\mathrm{x}\)-axis)

1 \(\sqrt{(\pi+2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi}\) with \(x\) - axis
2 \(\sqrt{(\pi-2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi-2}\) with \(x\) - axis
3 \(\sqrt{(\pi-2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi}\) with \(x\) - axis
4 \(\sqrt{(\pi+2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi-2}\) with \(x\) - axis
Motion in Plane

269947 A particle starts from the origin at \(t=0 \mathrm{~s}\) with a velocity of \(10.0 \hat{j} \mathbf{~ m} / \mathrm{s}\) and moves in the \(x y\)-plane with a constant acceleration of \((8 \hat{i}+2 \hat{j}) \mathrm{ms}^{-2}\). Then \(y\)-coordinate of the particle in \(2 \mathrm{sec}\) is

1 \(24 \mathrm{~m}\)
2 \(16 \mathrm{~m}\)
3 \(8 \mathrm{~m}\)
4 \(12 \mathrm{~m}\)
Motion in Plane

269948 A car moving at a constant speed of \(36 \mathrm{kmph}\) moves north wards for 20 minutes then due to west with the same speed for \(8 \frac{1}{3}\) minutes. what is the average velocity of the car during this run in \(\mathbf{k m p h}\)

1 27.5
2 40.5
3 20.8
4 32.7
Motion in Plane

269949 Velocity of a particle at time \(t=0\) is \(2 \mathrm{~ms}^{-1}\). A constant acceleration of \(2 \mathrm{~ms}^{-2}\) acts on the particle for 1 second at an angle of \(60^{\circ}\) with its initial velocity. Find the magnitude of velocity at the end of 1 second.

1 \(\sqrt{3} \mathrm{~m} / \mathrm{s}\)
2 \(2 \sqrt{3} \mathrm{~m} / \mathrm{s}\)
3 \(4 \mathrm{~m} / \mathrm{s}\)
4 \(8 \mathrm{~m} / \mathrm{s}\)
Motion in Plane

269946 The displacement of the point of a wheel initially in contact with the ground when the wheel rolls forward quarter revolution where perimeter of the wheel is \(4 \pi \mathrm{m}\), is (Assume the forward direction as \(\mathrm{x}\)-axis)

1 \(\sqrt{(\pi+2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi}\) with \(x\) - axis
2 \(\sqrt{(\pi-2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi-2}\) with \(x\) - axis
3 \(\sqrt{(\pi-2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi}\) with \(x\) - axis
4 \(\sqrt{(\pi+2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi-2}\) with \(x\) - axis
Motion in Plane

269947 A particle starts from the origin at \(t=0 \mathrm{~s}\) with a velocity of \(10.0 \hat{j} \mathbf{~ m} / \mathrm{s}\) and moves in the \(x y\)-plane with a constant acceleration of \((8 \hat{i}+2 \hat{j}) \mathrm{ms}^{-2}\). Then \(y\)-coordinate of the particle in \(2 \mathrm{sec}\) is

1 \(24 \mathrm{~m}\)
2 \(16 \mathrm{~m}\)
3 \(8 \mathrm{~m}\)
4 \(12 \mathrm{~m}\)
Motion in Plane

269948 A car moving at a constant speed of \(36 \mathrm{kmph}\) moves north wards for 20 minutes then due to west with the same speed for \(8 \frac{1}{3}\) minutes. what is the average velocity of the car during this run in \(\mathbf{k m p h}\)

1 27.5
2 40.5
3 20.8
4 32.7
Motion in Plane

269949 Velocity of a particle at time \(t=0\) is \(2 \mathrm{~ms}^{-1}\). A constant acceleration of \(2 \mathrm{~ms}^{-2}\) acts on the particle for 1 second at an angle of \(60^{\circ}\) with its initial velocity. Find the magnitude of velocity at the end of 1 second.

1 \(\sqrt{3} \mathrm{~m} / \mathrm{s}\)
2 \(2 \sqrt{3} \mathrm{~m} / \mathrm{s}\)
3 \(4 \mathrm{~m} / \mathrm{s}\)
4 \(8 \mathrm{~m} / \mathrm{s}\)
Motion in Plane

269946 The displacement of the point of a wheel initially in contact with the ground when the wheel rolls forward quarter revolution where perimeter of the wheel is \(4 \pi \mathrm{m}\), is (Assume the forward direction as \(\mathrm{x}\)-axis)

1 \(\sqrt{(\pi+2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi}\) with \(x\) - axis
2 \(\sqrt{(\pi-2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi-2}\) with \(x\) - axis
3 \(\sqrt{(\pi-2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi}\) with \(x\) - axis
4 \(\sqrt{(\pi+2)^{2}+4}\) along \(\tan ^{-1} \frac{2}{\pi-2}\) with \(x\) - axis
Motion in Plane

269947 A particle starts from the origin at \(t=0 \mathrm{~s}\) with a velocity of \(10.0 \hat{j} \mathbf{~ m} / \mathrm{s}\) and moves in the \(x y\)-plane with a constant acceleration of \((8 \hat{i}+2 \hat{j}) \mathrm{ms}^{-2}\). Then \(y\)-coordinate of the particle in \(2 \mathrm{sec}\) is

1 \(24 \mathrm{~m}\)
2 \(16 \mathrm{~m}\)
3 \(8 \mathrm{~m}\)
4 \(12 \mathrm{~m}\)
Motion in Plane

269948 A car moving at a constant speed of \(36 \mathrm{kmph}\) moves north wards for 20 minutes then due to west with the same speed for \(8 \frac{1}{3}\) minutes. what is the average velocity of the car during this run in \(\mathbf{k m p h}\)

1 27.5
2 40.5
3 20.8
4 32.7
Motion in Plane

269949 Velocity of a particle at time \(t=0\) is \(2 \mathrm{~ms}^{-1}\). A constant acceleration of \(2 \mathrm{~ms}^{-2}\) acts on the particle for 1 second at an angle of \(60^{\circ}\) with its initial velocity. Find the magnitude of velocity at the end of 1 second.

1 \(\sqrt{3} \mathrm{~m} / \mathrm{s}\)
2 \(2 \sqrt{3} \mathrm{~m} / \mathrm{s}\)
3 \(4 \mathrm{~m} / \mathrm{s}\)
4 \(8 \mathrm{~m} / \mathrm{s}\)