Question Paper
PART- A : PHYSICS
1. A uniform cylinder of length L and mass M having cross - sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density σ at equilibrium position. The extension x0 of the spring when it is in equilibrium is : (1) Mg k (2) Mg LA 1 kM σ ⎛⎞ − ⎜⎟ ⎝⎠ (3) Mg LA 1 k 2M σ ⎛⎞ − ⎜⎟ ⎝⎠ (4) Mg LA 1 kM σ ⎛⎞ + ⎜⎟ ⎝⎠ (Here, k is spring constant) 1. (3) 0 LA Kx g mg 2 ⎛⎞ + σ = ⎜⎟ ⎝⎠ ∴ x0 = Mg LA 1 k 2M α ⎛⎞ − ⎜⎟ ⎝⎠ 2. A metallic rod of length ‘’ is tied to a string of length 2 and made to rotate with angular speed ω on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ‘B’ in the region, the e.m.f. induced across the ends of the rod is : (1)
22B 2 ω (2) 2 3B 2 ω (3) 2 4B 2 ω (4) 2 5B 2 ω
2. (4) V = () 3 2 v B d x Bdx × ⋅ = ω ∫∫ V =
25B 2 ω
3. This question has statement I and Statement II. Of the four choice given after the statements, choose the one that best describes the two statements. Statement – I : A Point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as 21m f mv thenf 2 M m ⎛ ⎞ ⎛ ⎞ = ⎜ ⎟ ⎜ ⎟ + ⎝ ⎠ ⎝ ⎠ . Statement – II : Maximum energy loss occurs when the particles get stuck together as a result of the collision. (1) Statement - I is true, Statement - II is true, statement - II is a correct explanation of Statement - I (2) Statement - I is true, Statement - II is true, statement - II is not a correct explanation of Statement – I (3) Statement - I is true, Statement - II is false (4) Statement – I is false, Statement – II is true
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ω ga JEE-MAIN 2013 : Paper and Solution (4)
(Pg. 4)
3. (4) Maximum energy loss when inelastic collision takes place mv = (m + M) v′ v′ = m v mM + 2 i 1 k mv 2 = 22 22 f 2 1 1 m v 1 m k (m M)v' (m M) mv 2 2 2 M m (m M)
1. A uniform cylinder of length L and mass M having cross - sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density σ at equilibrium position. The extension x0 of the spring when it is in equilibrium is : (1) Mg k (2) Mg LA 1 kM σ ⎛⎞ − ⎜⎟ ⎝⎠ (3) Mg LA 1 k 2M σ ⎛⎞ − ⎜⎟ ⎝⎠ (4) Mg LA 1 kM σ ⎛⎞ + ⎜⎟ ⎝⎠ (Here, k is spring constant) 1. (3) 0 LA Kx g mg 2 ⎛⎞ + σ = ⎜⎟ ⎝⎠ ∴ x0 = Mg LA 1 k 2M α ⎛⎞ − ⎜⎟ ⎝⎠ 2. A metallic rod of length ‘’ is tied to a string of length 2 and made to rotate with angular speed ω on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ‘B’ in the region, the e.m.f. induced across the ends of the rod is : (1)
22B 2 ω (2) 2 3B 2 ω (3) 2 4B 2 ω (4) 2 5B 2 ω
2. (4) V = () 3 2 v B d x Bdx × ⋅ = ω ∫∫ V =
25B 2 ω
3. This question has statement I and Statement II. Of the four choice given after the statements, choose the one that best describes the two statements. Statement – I : A Point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as 21m f mv thenf 2 M m ⎛ ⎞ ⎛ ⎞ = ⎜ ⎟ ⎜ ⎟ + ⎝ ⎠ ⎝ ⎠ . Statement – II : Maximum energy loss occurs when the particles get stuck together as a result of the collision. (1) Statement - I is true, Statement - II is true, statement - II is a correct explanation of Statement - I (2) Statement - I is true, Statement - II is true, statement - II is not a correct explanation of Statement – I (3) Statement - I is true, Statement - II is false (4) Statement – I is false, Statement – II is true
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x
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ω ga JEE-MAIN 2013 : Paper and Solution (4)
(Pg. 4)
3. (4) Maximum energy loss when inelastic collision takes place mv = (m + M) v′ v′ = m v mM + 2 i 1 k mv 2 = 22 22 f 2 1 1 m v 1 m k (m M)v' (m M) mv 2 2 2 M m (m M)