A physical quantity \(P\) is related to four observations \(a,b,c\) and \(d\) as follows:
\(P=\dfrac{a^3b^2}{c\sqrt{d}}\)
The percentage errors of measurement in \(a,b,c\) and \(d\) are \(1\%,3\%,2\%\) and \(4\%\) respectively. The percentage error in the quantity \(P\) is:
\(P=\dfrac{a^3b^2}{c\sqrt{d}}\)
The percentage errors of measurement in \(a,b,c\) and \(d\) are \(1\%,3\%,2\%\) and \(4\%\) respectively. The percentage error in the quantity \(P\) is:
| 1. | \(13\%\) | 2. | \(15\%\) |
| 3. | \(10\%\) | 4. | \(2\%\) |
Subtopic: Errors |
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Level 2: 60%+
NEET - 2025
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Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its \(10\) Vernier Scale Divisions (V.S.D.) are equal to its \(9\) Main Scale Divisions (M.S.D.). The least division in the M.S. is \(0.1\text{ cm}\) and the zero of V.S. is at \(x=0.1~ \text{cm}\) when the jaws of Vernier callipers are closed. If the main scale reading for the diameter is \({M}=5~\text{cm}\) and the number of coinciding vernier division is \(8 ,\) the measured diameter after zero error correction, is:
| 1. | \(4.98 ~\text{cm}\) | 2. | \(5.00 ~\text{cm}\) |
| 3. | \(5.18 ~\text{cm}\) | 4. | \(5.08 ~\text{cm}\) |
Subtopic: Measurement & Measuring Devices |
Level 3: 35%-60%
NEET - 2025
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A balloon is made of a material of surface tension \(S\) and its inflation outlet (from where gas is filled in it) has small area \(A.\) It is filled with a gas of density \(\rho\) and takes a spherical shape of radius \(R.\) When the gas is allowed to flow freely out of it, its radius \(r\) changes from \(R\) to \(0\) (zero) in time \(T.\) If the speed \(v(r)\) of gas coming out of the balloon depends on \(r\) as \(r^a\) and \(T \propto S^\alpha A^\beta \rho^\gamma R^\delta\) then:
| 1. | \(a=-\dfrac{1}{2},~ \alpha=-\dfrac{1}{2}, ~\beta=-1, ~\gamma=\dfrac{1}{2},~ \delta=\dfrac{7}{2}\) |
| 2. | \(a=\dfrac{1}{2},~\alpha=\dfrac{1}{2},~ \beta=-\dfrac{1}{2}, ~\gamma=\dfrac{1}{2},~ \delta=\dfrac{7}{2}\) |
| 3. | \(a=\dfrac{1}{2}, ~\alpha=\dfrac{1}{2}, ~\beta=-1, ~\gamma=+1, ~\delta=\dfrac{3}{2}\) |
| 4. | \(a=-\dfrac{1}{2}, ~\alpha=-\dfrac{1}{2}, ~\beta=-1, ~\gamma=-\dfrac{1}{2}, ~\delta=\dfrac{5}{2}\) |
Subtopic: Dimensions |
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Level 3: 35%-60%
NEET - 2025
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In some appropriate units, time \((t)\) and position \((x)\) relation of a moving particle is given by \(t=x^2+x. \) The acceleration of the particle is:
| 1. | \(+\dfrac{2}{(x+1)^3}\) | 2. | \(+\dfrac{2}{(2x+1)}\) |
| 3. | \(-\dfrac{2}{(x+2)^3}\) | 4. | \(-\dfrac{2}{(2x+1)^3}\) |
Subtopic: Non Uniform Acceleration |
Level 3: 35%-60%
NEET - 2025
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Two cities \(X \) and \(Y\) are connected by a regular bus service with a bus leaving in either direction every \(T~\text{min}.\) A girl is driving scooty with a speed of \(60~\text{km/h}\) in the direction \(X\) to \(Y\) notices that a bus goes past her every \(30~\text{minutes}\) in the direction of her motion, and every \(10~\text{minutes}\) in the opposite direction. Choose the correct option for the period \(T\) of the bus service and the speed (assumed constant) of the buses.
| 1. | \(10 ~\text{min},~ 90~ \text{km/h}\) | 2. | \(15 ~\text{min},~ 120~ \text{km/h}\) |
| 3. | \(9 ~\text{min},~ 40~ \text{km/h}\) | 4. | \(25 ~\text{min},~ 100~ \text{km/h}\) |
Subtopic: Relative Motion in One Dimension |
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Level 3: 35%-60%
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A ball of mass \(0.5~\text{kg}\) is dropped from a height of \(40~\text{m}.\) The ball hits the ground and rises to a height of \(10~\text{m}.\) The impulse imparted to the ball during its collision with the ground is:
(take \(g=9.8~\text{m/s}^2\))
(take \(g=9.8~\text{m/s}^2\))
| 1. | \(0\) | 2. | \(84~\text{N-s}\) |
| 3. | \(21~\text{N-s}\) | 4. | \(7~\text{N-s}\) |
Subtopic: Newton's Laws |
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Level 3: 35%-60%
NEET - 2025
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There are two inclined surfaces of equal length \((L)\) and same angle of inclination \(45^\circ\) with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes \(2\) times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction \((\mu_k)\) between the object and the rough surface is close to:
| 1. | \(0.5\) | 2. | \(0.75\) |
| 3. | \(0.25\) | 4. | \(0.40\) |
Subtopic: Friction |
52%
Level 3: 35%-60%
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The kinetic energies of two similar cars \(A\) and \(B\) are \(100~\text J\) and \(225~\text J\) respectively. On applying brakes, car \(A\) stops after \(1000~\text m\) and car \(B\) stops after \(1500~\text m.\) If \(F_A\) and \(F_B\) are the forces applied by the brakes on cars \(A\) and \(B,\) respectively, then the ratio \(\dfrac{F_A}{F_B}\) is:
| 1. | \(\dfrac{1}{3}\) | 2. | \(\dfrac{1}{2}\) |
| 3. | \(\dfrac{3}{2}\) | 4. | \(\dfrac{2}{3}\) |
Subtopic: Work Energy Theorem |
58%
Level 3: 35%-60%
NEET - 2025
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A bob of heavy mass \(m\) is suspended by a light string of length \(l.\) The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point \(P\) making an angle \(\theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point \(P\) to its initial speed \(v_0\) is:
| 1. | \(\left(\dfrac{\cos \theta}{2+3 \sin \theta}\right)^{-1 / 2}\) | 2. | \(\left(\dfrac{\sin \theta}{2+3 \sin \theta}\right)^{1 / 2}\) |
| 3. | \((\sin \theta)^{1 / 2}\) | 4. | \(\left(\dfrac{1}{2+3 \sin \theta}\right)^{1 / 2}\) |
Subtopic: Conservation of Mechanical Energy |
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Level 3: 35%-60%
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The sun rotates around its centre once in \(27\) days. What will be the period of revolution if the sun were to expand to twice its present radius without any external influence? Assume the sun to be a sphere of uniform density.
| 1. | \(115\) days | 2. | \(108\) days |
| 3. | \(100\) days | 4. | \(105\) days |
Subtopic: Angular Momentum |
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Level 2: 60%+
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