The dimensional formula for torque is same as MCQ with Answer and Explanation
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Question #1
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The centre of mass of a uniform semicircular ring of radius R lies at distance from centre
Question #2
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Which scientist famously demonstrated that a changing magnetic field induces an electromotive force (EMF), discovering electromagnetic induction?
Correct Answer: Option A
Explanation:
Michael Faraday discovered electromagnetic induction. He showed that moving a magnet through a coil of wire, or changing the magnetic flux in one coil near another, induces an electrical current. Lenz's law later described the direction of that induced current. Maxwell formulated the classical theory of electromagnetic radiation.
Michael Faraday discovered electromagnetic induction. He showed that moving a magnet through a coil of wire, or changing the magnetic flux in one coil near another, induces an electrical current. Lenz's law later described the direction of that induced current. Maxwell formulated the classical theory of electromagnetic radiation.
Question #3
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A bullet of mass 20 g is fired from a gun of mass 2 kg with velocity 300 m/s. The recoil velocity of the gun is:
Correct Answer: Option A
Explanation:
By conservation of momentum: initial momentum = 0 (system at rest). Final momentum: m_bullet×v_bullet + m_gun×v_gun = 0. Thus (0.02 kg)(300 m/s) + (2 kg)(v_gun) = 0 ⇒ 6 + 2v_gun = 0 ⇒ v_gun = -3 m/s. Magnitude is 3 m/s; negative sign indicates opposite direction to bullet. This demonstrates momentum conservation in isolated systems. Memory tip: Recoil velocity = -(m_bullet/m_gun)×v_bullet. Such numerical problems test application of conservation laws, frequently appearing in competitive exams with varying mass ratios and velocities.
By conservation of momentum: initial momentum = 0 (system at rest). Final momentum: m_bullet×v_bullet + m_gun×v_gun = 0. Thus (0.02 kg)(300 m/s) + (2 kg)(v_gun) = 0 ⇒ 6 + 2v_gun = 0 ⇒ v_gun = -3 m/s. Magnitude is 3 m/s; negative sign indicates opposite direction to bullet. This demonstrates momentum conservation in isolated systems. Memory tip: Recoil velocity = -(m_bullet/m_gun)×v_bullet. Such numerical problems test application of conservation laws, frequently appearing in competitive exams with varying mass ratios and velocities.
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